Player gets injured every week in Manager Mode

At this point, games released for the PS2 are so far down a publisher's/developer's priority list that they might as well not exist. People have reported framerate issues and gameplay problems, although others were happy with everything except the graphics, which you note aren't that important to you.

I can't find a side-by-side review, or a review of the multiplayer support, (or even a professional review of the PS2 version, period!) so I can't answer that part of your question directly. However, the publisher's site lists 3 features on the PS2 version versus 12 for the PS3 version, so it's safe to assume that the PS2 version is relatively stripped down compared to the PS3 version.

Since you paid money to upgrade to the Playstation 3, and you're paying money to play the latest iteration of the franchise, why not spend a few dollars more on the game to make sure you get the best experience possible?

Try not to sprint or run once your energy bar is depleted. Your stamina will decrease very quickly. Use running and sprinting in bursts rather than all the time; once the energy bar has gone down, let it replenish before doing anything else strenuous! while at zero, your energy level severely affects your stamina.

Also, how to increase your virtual pro's physical attributes (including stamina): http://forums.electronicarts.co.uk/fifa-10-sony-playstation-3-microsoft-xbox-360/828314-virtual-pro-accomplishments.html (under the "physical" heading)