well, actually it has both. If you ever played BG with him it shows tables just for that type of game and under those indeed come tables with all of your games against that player...
I personally think that profile page is a bit messy. I ask one information and it still shows me everything else... (it took me a while before I realized the "show games against me only" link was working, because whenever I clicked it I just saw the fellowships (only the next day I bothered to scroll the page down! )

And now here comes a feature request:
--8--8--8--8--
Can the profile page be sorted into tabs (like the Settings page, for instace)?
(Personal Info, Fellowships, All Finished Games, Games against Me, Torunaments, Unfinished Games, etc, etc, etc)
I think it would even take some load of the server because it wouldn't have to sed me all that info at once when all I want to know is that person's name or gender as often happens...