I'm 25 right now and I have been living in New York for the past year. Prior to that, I spent the past two and a half years in San Francisco (from when I was 22 to 24). I like both cities and often go back and forth between which I prefer (and yes, the weather certainly has some sway on who I'd pick on a given day).
I'll share my personal perspective, but ultimately no one can answer this question but you yourself (the good thing is you're choosing between the two most desirable cities in US, so you can't really go wrong either way).
These are the things that matter a lot to me as an early 20-something: career, livability/commute, culture, relationships, nightlife, and geography.
I work in the tech industry as a product designer, and I don't buy that if you want to work in tech you need to live in San Francisco. If you're in technology, then you're well equipped with the internet and know that you can build a career pretty much anywhere in the world. That said, I do think that starting a career in tech is easier in San Francisco. Starting out in SF, I had access to a lot of experienced designers who became really great mentors. I had a strong network of friends who were designers and developers that I met at the plethora of industry events being held in the city (there's seriously something every few days). I got even more experience because outside of my day job it was so easy to find people to work on side projects with. There's also more opportunities, more companies, and people are generally more open minded to the idea of moving around.
I don't know your specific career, so I won't drill too much into this, but I do believe the design culture in San Francisco is more developed than it is New York.
People in New York who work in tech do not live and breathe their jobs the way they do in San Francisco. For many being a developer or designer is just that; a job. People here seem to take a lot of pride in having diverse friend groups (in which your friends aren't all also designers or developers). A side project for someone in New York probably doesn't mean building another app, it means playing gigs/shows to fulfill their musical interests, or pickling things, or home-brewing. Which is not to say that people in SF don't do these things, but there's a lot more pride in the idea of exploration and diverse interests rather than developing deep expertise. There are many promising and successful startups in New York, many of which straddle the line with other stronghold New York industries like finance, nightlife, fashion, and media. For example, I now know a lot more than I ever did about the publishing/journalism industry from working at BuzzFeed.
The last SF apartment I lived in was a one bedroom by myself which I scored for $1,800/month and was two blocks from Alamo Square park. I definitely regretted giving up that apartment when I moved to New York. Though, from what I've heard and read, it would be very hard to get a one bedroom for that price in San Francisco today.
When I first moved to New York, I decided I wanted to live in downtown Manhattan so I could be close to work and the popular neighborhoods to go out in. I paid over $2,000 a month for a one room studio (no enclosed kitchen), one tiny closet, and an even tinier bathroom in which you have one square foot to stand in. I just moved to Williamsburg and am paying the same amount as before but I have more space, a separate kitchen, walk-in closet, and in a new building with crazy amenities (like an indoor basketball court, wut!). My commute is only ten minutes longer. So, despite what many believe, it is feasible to live alone in New York at age 25 if roommates aren't your jam. Similar to San Francisco, the further out you go, the more bang you get for your buck, at the sacrifice of commute and nightlife. Given the current housing market in San Francisco, I would rank the two cities as equal.
New York wins hands down. You can get anywhere via the subway, sometimes it just takes a few transfers. It's far more reliable and the trains are quite frequent. Taxis are also prolific and pretty affordable so no need to resort to Uber or Lyft as often. When I lived in San Francisco and moved out of the Mission, I was at the mercy of the Muni bus system, which was hell on earth. My commute is about 20 minutes and actually shorter now than it was in SF even though I live farther from my office in New York. The more expansive subway system also opens up a lot more options for housing.
If you like the idea of diversity, you can't beat New York. It is a socio-economic melting pot. Not to say that there aren't issues (Stop and Frisk), but we don't have the serious class tension currently present in San Francisco today (things had not reached a boiling point yet when I lived there). New York has so many neighborhoods that still (despite gentrification) reflect charming characteristics of the various groups that immigrated there. There's a ethnic restaurant for any type of cuisine imaginable, no matter how niche, and food in general is very good and much cheaper than in San Francisco.
I also like going to art museums and while I feel there is definitely an appreciation for art in San Francisco, you can easily hit up all the museums pretty quickly. I still haven't been to half the museums in New York. I liked that San Francisco has a few really big events that much of the city comes together for (like Bay to Breakers or SF Pride), but on the flip side there are lot more one-off street festivals or events going on in New York.
I actually give this category to San Francisco. Nightlife in New York includes clubs/trendy bars in the Meatpacking District, which I feel completely out of place in. There's cocktails bars, but they feel more suited for a date. When your friends live in different boroughs and there's inclement weather, it's definitely hard to get a group of friends out. In addition, because the apartments are so tiny, there are very few house parties. I prefer the bars in San Francisco like Madrone, Beauty Bar, or Make Out Room, which seemed to straddle the line between a dance club and a dive bar. The amount of concerts to attend that were of interest to me in SF/NY are pretty much even.
For friendships, I'm biased towards San Francisco because the majority of my college friends moved there as well and I developed many friendships straight out of college there. However, people in San Francisco are notorious for blowing off plans to meet up (). From my experience, this is no exaggeration and I personally had a hard time dealing with it. I like that in New York people are more committed to their plans, or simply more upfront if they don't think they'll make it in the first place. In New York, it's also more difficult to mix friend groups than it was in San Francisco, perhaps because of that diversity (you have your work friends, your college friends, your hobby friends). Some people might prefer that distinction.
For dating, it depends. As a straight woman, I think San Francisco is an easier city to meet men in and if you're a straight man, then New York is your oyster. I can't speak to what it's like for a gay man or woman. Ironically, the few dates I did go on in New York were almost always with men who were in town from San Francisco. Both cities are open minded about online dating. Even though New York gets a rep for being a single's city, I think people in San Francisco approach dating equally casually. The one thing I appreciate about New York is that it's certainly less incestuous. Your chances of working with an ex, or running into an ex, your friend dating an ex, or your exes all becoming drinking buddies is much slimmer.
Traveling is one of my favorite hobbies, so this category is important to me. I do miss the amount of fun day or weekend trip options from San Francisco. You can get out of the city by simple trips to the surrounding area like Napa, Sausalito, Tomales Bay, Santa Cruz etc ... or easily go a little further for a weekend to Los Angeles, Portland, or Seattle. One time, my best friend and I spontaneously took a weekend roadtrip to Disneyland. It's that easy. I don't feel like there are as many immediate options near New York that are as appealing. For international travel, it's a dead split to me. San Francisco is much easier to access Asia from and on the flip side New York is perfect for easy access to Europe.
Bonus Category: Summer
I moved to New York in January and by April, I was sure that I would want to move back to San Francisco at the end of the year/my lease ... and then, summer happened. Summer in New York is amazing. Everyone sheds their winter-borne antisocial habits and the whole city is energetic. Even if you're an adult with a full-time job, it still feels like you're a kid enjoying your summer break. It is totally worth the single digit weather I am suffering through right now. You can even walk around at night in short shorts and flip flops without the prerequisite light sweater you will need to carry year round in San Francisco.
I don't think New York is forever, and I see myself moving back to San Francisco in a few years or later in life ... but right now I'm pretty happy in New York.
And with that, now you know all the details of my early adulthood...More questions on Music: