budget cards are all trash so 'most powerful budget card' is pointless, but i'd be willing to bet that nvidia cards are basically just as powerful as ATI cards at the same price point
midrange the GTX260 beats the 4870 since they introduced the core 216 model and is about $20 cheaper on average
high range i dont know at all because youre an idiot if you buy that shit
compatibility with other AMD hardware is pointless because nobody buys amd over an intel right now unless youre an idiot with too much brand loyalty to amd (literally if you buy an amd over a core i7 youre bad person)
ATI chips have really bad hardware video acceleration, they only supprt like 1 bluray x264 profile (meaning no bluray rips will be hardware accelerated, it has to be exactly whats on a bluray disc) whereas nvidia chips support a wide variety of formats and resolutions
maybe next generation ATI will come out ahead (doubtful because fermi is going to own) but for now buy nvidia.
i don't know if you're just clowning about but this is pretty silly. idiots buy high range and budget cards, the HD5770 is a budget card that nearly as powerful as the core 216 that's cheaper and does direct x 11
compatibility with other AMD hardware is an advantage because amd make more than cpus; the dragon platform is synergistic. in terms of cpu alone the topic is talking about a replacement in a computer he already has, but here are some situations in which an AMD cpu may be a smart choice over a core i7:
-you're building a budget rig (the cheapest core i7 here is ~$200 more than the most expensive phenom II)
-you're building a gaming rig (the cpu is rarely the limiting factor in gaming, extra cash goes to graphics)
-you're building an HTPC (amd integrated graphics are insane in terms of HD stuff)
-you're likely to want to upgrade your cpu without changing your motherboard (intel has more sockets than transistors)
i don't even know what you're talking about that it only supports one h.264 profile unless you mean it supports only bluray profile 1, which doesn't mean what you said it does and is also wrong as avivo hd supports profile 1.1
AMD stuff is still an option, though if you have the cash and desire for BEST AVAILABLE you're going to want an intel chip with a nvidia card or two.