WARNING: LONG RAMBLING OPINIONS AHEAD
Maybe the main point here is that tactics need to be based on more than an ideal, i.e. the players at your disposal, the opposition, the weather, the state of the pitch, etc. Although it may seem "admirable" to insist on your philosophy, there are plenty of times where it just indicates your unwillingness or inability to adapt. It's always been Wenger's Achilles heel, but he's been able to manipulate his environment enough in the past to impose his philosophy. He's lost that ability, in large part due to financial issues but also because his own ability to do so has faded. His tactical inflexibility on match days is indicative of that.
That being said, if he had more control (i.e. a fuckload of money or a special knowledge of an unknown talent pool) he might be able to impose his philosophy again. He also has obviously changed tremendously from a more infuriating tikki-takka style back to something more like our pre-2007 squads. It just takes him so bloody long to change what so much of us have known needed doing for years.
Chelsea on the other hand are like the opposite of us, they have no culture at their club except cuntiness, they win by having managers that are willing and able to tactically adapt to situations. As soon as they try to impose a philosophy or footballing culture at the club, however, Roman takes a dislike to them and kicks them out.
They're a shit club all-around filled with mercenaries and a revolving managerial door, but financial clout and tactical flexibility based on achieving a few crucial results due to job uncertainty has seen them pick up a few trophies along the way. It's a strategy for winning, but look how confused the fans are and how miserable relations are within the club.
I don't think it's quite fair to use "negative" football, catenaccio, and the counter-attacking style interchangeably, as if they are the same. They aren't:
Negative football isn't necessarily based on having limited possession as Biggus has pointed out. In fact, I'd say that negative football actively uses strategies that are not within the spirit of the rules of the game to prevent losing (and I guess to win if possible), i.e. teams that systematically foul and annoy while paying little attention to the ball itself, teams that are more focused on messing with the opposition than playing football, teams that need a towel to take a throw-in, etc. They often don't have a lot of possession, but that's not necessarily the main point. All teams do this to some extent, but sometimes teams rely on it, and I'd call that "negative" football.
Catenaccio no longer exists today, really. They idea of prioritising the defense exists, but that's about all that remains. There are no sweepers, and no back line in the world only uses man-marking. Catenaccio was about being systematic in organising the defense with a mind to create openings in the other team, almost like shepherding opposition players until the opportunity to score presented itself. I wouldn't call it negative as that really isn't fair. It's may not be a high scoring strategy, but it can be effective with the right players, and I don't doubt that it could have been enjoyable to watch.
Counterattacking is arguably the most exciting and entertaining brand of football out there right now, imo. It assumes a shape that asks the opposition players to cross the halfway line, at which point they are pressed until the ball is won and forwards are released. It prioritises attack, as the name suggests, so naturally it uses the concept of defending in service to that. It's not really similar to catenaccio because instead of defending ultra-deep you press higher up the pitch. It's a much higher energy, higher tempo game. It also relies on taking shots from outside the box to force the opposition to step forwards if they themselves are catennacio-ing. It also takes risks, which makes it exciting, because the other team needs to be stretched and pulled further from their goal to make enough space to counter. Finding the balance between risky and kami is tough.
Anyway, I think it's important to make those distinctions. I think we currently use a hybrid counterattacking/possession game, which is actually ideal if the manager or players had any confidence in it (it's how Dortmund and Bayern play, for instance). It's taken a long time to get back to this sort of football, and I'm glad we're getting there, but it's often more theoretical than a reality. We often fail to execute, and the players need someone instructing them on the touchline, not huddled in a ball biting his fingernails hoping it all works out.
I don't think we could play "negative" football with the players we have, or catennacio for that matter. We've seen that we can't play a pure possession game either. Man United have used a wing-play style with a compact defense under Fungus and I don't think we could do that either. Basically, I think we're on the right track, but the players and the manager aren't getting the execution right, and too often revert to a bastardized version of a possession game that is boring and, more importantly, fails to win us games. Ideally, we could move up an down the scale from "possession" to "counterattacking" at will, depending on how we were faring and what the other team was doing. Too often we play right into their hands, especially in one-off cup games.
TL; DR: It doesn't really matter what tactic you use, but tactics are all that matter.