Red Faction II is probably the best First-Person Shooter on the PS2 to date. This is much better than the first Red Faction. Basically, in terms of Multiplayer AND Single-player this game is THE game to get.
Multiplayer-wise, I'd recommend RFII over most FPS for PS2 because the multiplayer in this game is much more deeper than in any other FPS (thats not online). Most shooters only have co-op and/or one-on-one deathmatch while RFII has many multiplayer modes and more variety with games such as Bagman (Tag), CTF, Regime, etc. (along with the standard Deathmatch and Arena Modes)
From a single-player standpoint I'd highly recommend RFII above any other FPS because the story gives you more reason to play through the whole campaign and contains more action than puzzle solving. A lot of other FPS's (like Timesplitters 2) single-player campaign has more puzzles and less action than RFII but has an equally good story compared to RFII.
So...basically, if you want an FPS with a lot of action and a minimal amount of puzzles with AWESOME multiplayer get Red Faction II.