Every Hitman game in the series improves the gameplay of the previous one in some way. They'll refine what worked and make it better, and change/eliminate what didn't work. Except for Hitman: Absolution. Here, they've changed so many things, and removed things that worked, that it does not feel like a Hitman game anymore.
With the new disguise system, anyone that has the same disguise as you can recognise you. This renders disguises, one of the staples of the Hitman series, almost pointless. Let's say that you want to get into a heavily guarded area. If you dress as a guard, they'll spot you. If you dress as a maintenance guy, you're not allowed in the area. So it's not really worth the effort, and you tend to ignore disguises altogether.
The biggest deviation from previous games is that the levels are no longer big sandboxes. The maps are actually quite big, but they are divided into small, linear segments. Once you complete one segment, you cannot go back to that part of the map. So the game loop consist of sneaking from point A to point B to point C, and hopefully at the end of the level there will be some target to kill.
All of this combined means that there is no longer a "planning phase", in which you try to examine the level and come up with an elaborate plan to (optionally) find the right disguise and eventually assassinate your target. Instead, you simply go from point A to point B while crouching and avoiding enemies, as if you were playing a really bad Splinter Cell clone, until you move on to the next really short segment. Rinse and repeat until you reach the end of the level and kill your target (if there was one, which is often not the case).
The save system wasn't good in the previous games, but here they've managed to make it even worse. You cannot make any manual saves. Instead, you need to rely on predetermined checkpoints. These checkpoints are scarce, and many segments don't even have checkpoints. This makes the game very frustrating and repetitive, and discourages experimentation. In addition, if you need to reload a previous checkpoint, all the NPCs that you've killed, subdued, hidden, etc. will respawn... So the only point of checkpoints is to get you a bit closer to the end of the segment.
The new point system is permanently visible, and you can see in real time how it penalises you for any lethal or non-lethal take down. This pushes you to play in the way the developers intended, rather than in your preferred way. I think that the game is more enjoyable if you completely ignore this point system and just play it your way.
There is a massive emphasis in the story, in contrast to all the previous instalments of this series, in which the story has always been minimal, and really just an excuse to tie missions together, as the real draw of the Hitman games is the gameplay, rather than the story. Having said that, this could have been a nice change, providing that the story had been any good. Unfortunately, it's very cheesy, over the top, full of plot holes and poorly written characters.
In each mission you can recover some hidden piece of evidence, which is completely meaningless story-wise, and it's just there to provide some extra points and extra challenge.
There is an alternative game mode called Contracts, but the servers are now down. There are some online guides to spin up your own private server, though.
Don't get me wrong, not everything is bad in the game, I think the graphics look great, and the gun play is satisfying (but the game punishes you for it). But Hitman: Absolution is just not worth it, even though it goes on sale very often and you can get it heavily discounted (for £1.50 or so), it's still not worth it in my opinion: this is, at best, a very generic stealth-action game. Instead, you should either buy its predecessor (Hitman: Blood Money), which is also often on sale and even cheaper, and it's better in pretty much every single way except for the graphics. Alternatively, if you want to play a more modern Hitman game, you can give World of Assassination a go, which I haven't played yet, but it apparently goes back to the successful formula of the previous Hitman games.
