Assuming you're playing the PC version and have the PC for it, BF3 has far superior visuals, but the graphics in PS2 aren't too shabby either.
They play very similarly, but Planetside 2 is an MMO and therefore instead of the 64 players max you get with BF3 you can have hundreds and hundreds of players all battling at once in PS2 across a map that is 10x the size of the biggest map in BF3.
Basically, if you want dynamic combat that doesn't require you to suit up with an outfit and use teamwork, go with BF3. If you want sheer scale and far larger battles (and more unlocks), go with PS2.
PS2 is free, so it's not like you have to pass up buying BF3 to get it.