I would argue that the modernisation of stadiums and the move to all-seater stadiums did a lot to kill off 80's-style hooliganism. The teams themselves realised by the end of the old First Division that there was serious money to be made in football, especially if they could start attracting families.
I'd argue the all-seater stadia barely had an impact in and of itself. It was more the gentrification of football coupled with less-hostile policing that really made the difference. Terracing or rail seating works fine in Germany and in the non-league game, there isn't some magical thing about standing up that turns people into hooligans.
The policing of football compared to other sports still needs a bit of work. For example at the football if I want a beer at half-time I have to go down to the concourse on 40mins and join a queue, wait ages while the real-life version of the squeaky-voiced youth from The Simpsons struggles with the pump. Then I have to drink the beer in three or four gulps if I want to see the start of the second half. This isn't a good way to drink alcohol, so I tend not to bother. If I was at a rugby league game in the same stadium I could take my beer to my seat and take my time drinking it sensibly. As others have said, it's not as if rugby fans are perfectly behaved either.
I'd credit the proliferation of CCTV, mobile phones with video recording ability, police aircraft and drones which capture footage. Back in the 1990's if someone threw a punch at the football they would have likely got away with it unless directly in front of a copper. Now if someone did that, they might get away with it at the time, but they'd probably get an early morning call in the following weeks and find themselves in hot water. I believe this has killed real football hooliganism and made it an extremely fringe activity. That said, not that long ago I did see someone punch a lone and moronic opposition fan who decided to start chanting for his own team in a crowd of home fans, he hit the deck and everyone just walked-on like nothing had happened and I very much doubt the police caught up with the offender. I think if you don't engage in idiotic behaviour as a fan you are very unlikely to get caught up in anything, unless the game is policed by South Yorkshire Police.
What you still get a bit of is wannabe teenage 'hardmen*' who engage in posturing trying to live-out the 'romanticised glory days.' These are usually soon noticed by the police and aren't actually interested in violence anyway, they might hide behind police lines and give verbal abuse or throw a plastic bottle, but take the police away and they soon go quiet.
Most trouble at football is just drunken idiocy, no different to what goes on in most town centres on a Saturday night, but the policing, media and legislative response to anything involving football fans is much more severe.
Anyone interested in this subject and on Twitter should follow these two accounts, who tweet on the subject:
https://twitter.com/WeAreTheFSA https://twitter.com/FairCop_
*Usually about 8 stone wet through and wearing fake clobber that's too big for them.