Let's get one thing about Timesplitters 2 out of the way right off the bat: It is not, as the quote on the box says, 'The heir apparent to Goldeneye'. It's certainly closer to that title than Goldeneye: Rogue Agent was, but I wouldn't say Timesplitters 2 is in the same league as the truly top-notch first-person shooters.
Which isn't to say it can't be a lot of fun. It's a fairly simple game, with your character jumping to different time periods to collect crystals that will help you defeat the evil aliens in your time. To that end, you run through levels, killing people here, saving others there, occasionally needing to find a certain document or defuse a bomb. Nothing at all complicated or ground-breaking.
I'd say the strong points of the game are multiplayer and co-op mode. It's always nice to be able to play through a level with a friend, though some friends are more harm than help to have around, especially when stealth is required. And the game itself has some issues, mostly pertaining to the checkpoints. See, if Player A is lagging behind to do a serious search for hidden areas and ammo, and Player B charges ahead blindly to the checkpoint, A will be automatically warped to B's location, which can lead to confusion and annoyance, especially if there winds up being something back there you needed to find. Sadly, they still hadn't fixed that glitch by the time they released Timsplitters: Future Perfect. In fact, I think it was even worse in some ways, probably since the objectives were sometimes more complicated, and so abrupt shifting like that had a better chance of screwing you up. But, when the game's issues or your partner's inadequacies get you down, you can always switch to good, old, simple multiplayer and spend some time killing random foes, or the friend that's driving you nuts.
The multiplayer challenges are standard fare, with the free-for-alls, and capture the flag, and so on and so forth, as there's quite a few characters to choose from, each with varying levels of speed, agility, and resistance to damage. Plus you can mix and match which weapons are available in each level if you want, which adds a little more variation to the game. There's also Arcade mode, where you can take little challenges, like seeing how long you can stay alive against endless hordes of zombies, and trying to win trophies for high scores, which will also let you unlock levels or new characters to use in multiplayer, depending on circumstance.
Future Perfect isn't much different really, except they spent a little more time letting you get to know the main character, Leon, and adding humor to the game through the cutscenes. It's a contrast to Timesplitters 2, where Leon doesn't talk all that much, and he's very much a grim avenger time hero, while in Future Perfect he takes a more light-hearted, "this is fun!" approach to saving the universe, epitomized in his (horrific) catchphrase 'It's time to split!', which is usually met by awkward silence from whomever he's teamed up with in that time period. Which is basically how I'd react if someone said that to me. Well, that and running away from them very fast.