Better in what sense? I think both are ridiculous and will give you more trouble than they are worth.
Performance wise if you are talking about (3)5830's vs (2)5970's. That is easy, the two 5970's would roast the 5830's. However. What on EARTH could you possibly need with that much power unless you were driving at LEAST a 3+ display gaming setup?
Second comment is, once you get past 2 gpus many games do NOT scale well at all. In many cases not at all, so a 3rd 5830 would not get you much, and possibly a 2nd 5970 either since it is a 2 gpu card. A single 5970 will run any eyefinity (3 display) setup very well.
What on earth do you need a setup like this for? Maybe we can start with that. The cost will be alot different. (3) 5830 would run $900, a dual 5970 setup $1400 just for cards. In either case you are looking at a 1000W PSU and ALOT of case cooling. I am not a fan of the 5830 to begin with, for what performance it gives I would look at a GTX460 as it is cooler and overclocks FAR better. Please give us more info.
Why you want trifire HD5830?
Nvidia's cards (SLI) are scaled better than ATI (CF).
I agree in some cases. The new GTX460 is an SLI monster and scales at like 90% in some cases. SO awesome. The 5830 is a crippled 5870 an in my thoughts was a quick replacement for the 4890. The GTX460 is a card of it's own and reigns supreme at the $200 price point. The 5970 is a great card, I have one, but for $700 I could get similar performance from a pair of GTX460's. That is assuming your motherboard supports SLI, which will have a bearing on what you go with.
I like single card setups, less hassle, less heat issues, etc. I don't want a wind tunnel just to cool cards. I still want to know what the OP is trying to accomplish.