Atlantico: The AMD HD4870 was a top-of-the-line GPU in late 2008 and the 550 ti was a budget GPU in 2011, so instinct says the AMD GPU is the better one of the two.
Looking at the specs, the AMD has a 256bit memory bus, the nvidia has only 192bit bus, the AMD GPU will certainly run hotter (being a high-end item) but that's neither here nor there for a decent desktop machine.
Any top-of-the-line enthusiast GPU will run hotter than a budget GPU, at any time in any generation, as a rule of thumb.
Anyway, go with what you prefer, but all things being equal, a budget GPU (especially nvidia ones, see the recent gtx970 debacle) are gimped in one way or another.
But if you have the time, just test them.
I bought a 4870 when I built my pc in '08. I played every game without a hassle 'til 2012 on high'ish settings (when I gave it to my brother - for the record it died 1 year later, but he lives in way warmer parts than I do).
It's a card that consumme/heats a lot. If you have a self arranged, well ventilated case, and you don't have 40°C in summer you should be fine.
I beleive the 550 Ti has a better efficiency (perfs/consumption). Didn't play with one but the specs indicates that you probably will keep it longer if you are careful (monitoring, cleaning ..)
Edit : wrong quote. But I agree with you Atlantico :-)