Maybe I just read into things too deeply, but most of these are hard to determine when you really look at it...
Music: This is basically the first half of the 2000s vs. the back half of the 2010s. The late 2000s was the most trash era of all-time, in my opinion, but the early 2000s was such a classic period, and maybe my favorite in my own lifetime. The second half of the 2010s gave us widespread access to streaming services, and thus opened up the world of music to where you could discover unlimited fire. This is the closest category to me, but I would have to edge it to the 2000s on the strength of the several undeniable classics that came out in Neo-Soul and Hip-Hop.
Films: I gotta say the 2010s, because of Netflix and other services. 2000s movies weren't enough to combat this.
TV: I wanna say 2010s for the variety, but these huge shows with annoying ass fanbases (i.e., Game of Thrones, Walking Dead) really make me want to go against the 2010s. I'll have to say the 2000s. It had Chappelle's Show, prime Disney Channel, prime Cartoon Network & Adult Swim, and still had cool music shows like Rap City and the original 106 & Park.
Sports: I don't really watch sports that much anymore because its always been rigged, and I have better shyt to do. HOWEVER, I can objectively say that sports are more entertaining in the 2010s. We've seen Lebron for an entire decade, Black QBs are taking over football even more than the early '00s., and the internet has made sports conversation more entertaining.
Video Games: I stopped gaming years ago, so I'm not the best person to ask this. I personally have nostalgia about Grand Theft Auto and the old Maddens, but once again, I can't speak on today's games. Maybe they're better, I wouldn't know. However, based on my limited knowledge, I'd have to go with the 2000s.
Fashion: This is another tough one. The "popular" fashion was definitely better in the 2000s, but the 2010s are more open, which I love. By open, I mean that not everyone has to have the same style. You look at any rappers or young celebs nowadays, and you see all different styles of fashion. That wasn't really the case in the 2000s. For that reason, I have to edge it to the 2010s.
Politics: neither; fukk politics
Sex Symbols: This is the easiest on for me. I'm taking the 2000s, easily. Every bytch now has the same generic look. The 2000s had women with true sex appeal.
Cultural Shift: Another tough one... The 2000s saw the mass proliferation and ubiquity of the internet. However, the 2010s gave us the complete smartphone/app takeover. The 2000s had a huge shift in the music industry, due to "pirating" and labels/artists not making albums like they used to, because of that. The 2010s sought to rectify this problem with streaming and other online forms of paid consumption, and made music way more accessible. I don't think we'll truly know the cultural impact of the 2010s until a few years from now, but the 2000s laid the foundation for everything, tech-wise. I gotta say this one is a TIE
Although the 2010s has given us an abundance of both popular and independent music to enjoy, I give it to the 2000s just because it was the last era of true album and album-sale driven music. Back when even the most mediocre artist knew the importance of creating a complete piece of work as opposed to this streaming generation of pop hits. Not to mention there was more variety back then. You had both club and gangster hip hop taking over, independent hip hop acts like MF Doom or just about anyone that worked with Dilla were at the height of their success, Neo-Soul was an artistic alternative to the sexy flexy R&B of the time (which wasn't necessarily bad either), you had deep alternative rock bands like Coldplay, Garage Rock revival bands like the Strokes, and Nu Metal bands. And all of these genres were producing great ALBUMS not just pop hits on streaming platforms.
I don't know how anyone can say filmmaking was better in the 2000s. Pure nostalgia bias. 2000s films were terrible. The height of flashy, special effects consumerism over actual cinematography or performance artistry. For every Lord of the Rings, Kill Bill, Crouching Tiger, or No Country for Old Men it was a litany of bang bang, explosions and t*ts, cheesy CGI covered garbage.
TV definitely goes to the 2000s bro (though not by a huge margin). Not only was the 2000s more innovative television than the 2010s--The Sporanos, the Wire, Curb Your Enthusiasm, Walking Dead, and Breaking Bad alone kill damn near everything produced this decade--I would call the 2000s the golden age of television in general. The GOAT decade of television writing and production in my opinion. Game of Thrones is the one and only golden child of 2010s, besides a bunch of Netflix series that are apparently excellent.
Video games turned entirely into competitive multiplayer online games this decade. While the cinematic quality of games today is impressive, there is absolutely no comparing the fun and variety of video games then vs now. Genres that used to be staples of gaming platforms like mascot-platformers. fighters (besides Street Fighter), beat-em-ups and hack-and-slashers are all damn near dead outside of independent development houses. Companies that use to be staples of the industry like Sega and Konami have gotten rid of all their best talent and are far more interested in casino, coin-operated, and mobile gaming. The home market is dominated by generic competitive online games and cover-shooters. I stopped playing video games while I was in college.
2000s fashion was trizash. These kids dress better than we did.
Politics; seeing the first black President get elected after the Bush madness was unbelievable. Seeing him succeeded up by a racist reality TV star backed by cult-like fanaticism was an eye-opening shell shock. The madness, cheating, and corrupt revelations over the course of his Presidency has also been eye-opening, as well as the overall rise in right wing/nationalist movements all over the world. The way social media has influenced our political discourse has been notable as well. It's hard to pick which decade has had a greater impact, but I chose the 2000s because the election of the first black President after Bush, I feel, is what had the greater impact on politics afterwards. Obama's Presidency influenced all the madness happening today.
How you feel about 2010 sex symbols is how I feel about 2000s symbols. It was a generic glammy, club, fake-hair-and-nails-done look for everyone--not to mention lots of racial and cultural bias--while there is more variety and diversity in beauty today. Dark skin, light skin, tall, short, thick, petite all get love today, and everyone can have their own expression and style. I know some people hold their reservations about the Lizzos and Doja Cats of the world but the fact they can rise up to be symbols today I think is a good thing.
I'm with you on the conflicting cultural/tech shift.