Wouldn't know about the online component, but I do have both.
PES has more realism thats for sure. The ball seems more weighty, your player has to be in control of the ball if he's to do what you want, they've nailed the AI so there is actually a notable difference in players of varying calibre. You can pace your player, and changes of pace will fool opponents, and make taking them on a bit more realistic too. Theres a bit of a team manager mode to check out as well that's quite in depth... one thing you might notice in PES4 is that it's much harder to score against the computer/other-players than it is in FIFA games. Unless you're playing a limbless person with no knowledge of the sport, you'll probably find it a bit difficult to rack up high unrealistic scores. The game is awesome, and well worth owning...
...but FIFA is good too. It's more arcadey than PES, but not so much that it's like Virtua Striker or anything. The ball control is a little less realistic, but perhaps a little more friendly. There's a nice 'first touch' ability implimented on the second analog stick, which lets you tell your players what to do with the ball before they get it, so they can do it as soon as they get it. I personally feel free kicks are done better in FIFA, adding ball spin and stopping a power meter is simply more fun for me than PES' implimentation. The liscenced music and commentary is still crap. But it's not particularly good in PES4 either. FIFA too has a management mode. I'll be honest here - I have no interest in the team management modes of either game.
When it comes to multiplayer, I actually play both in equal measure. I play FIFA a lot with my brothers, but there are people who will refuse to play anything but PES4... so I hit that with them.