The answer is no, with caveats.
Nvidia and AMD's architecture have roughly equal potential if developers optimise for the hardware. However, Nvidia has been the force pouring money into GPGPU tools, software and projects. The effect of this is that most GPGPU products are made with Nvidia tools and hardware and with CUDA in mind. If they support AMD at all it is as an afterthought.
Nvidia's hardware is also easier to make reach its potential. Fermi has local caches, better support for high-level languages, and a simpler execution pipeline (AMD has 5 units per cluster, Nvidia has 1, so unoptimised software on AMD may not use all 5 units).
Also, CUDA will die in favour of cross-platform solutions; DirectCompute and OpenCL. Without huge subsidy by Nvidia, no one would tie themselves to a single-vendor protocol like CUDA. As the money has dried up as AMD began to 'win' in the consumer graphics space, we will see more projects shift to OpenCL and therefore not favour Nvidia any more. In 1-2 years I expect all new GPGPU apps to perform equally well on both, or even favour AMD if they continue to have better performing GPUs as now.
But:
Current apps, even Photoshop, are Nvidia optimised. You will get better GPGPU performance from Nvidia right now for most apps.
There is a problem though. Nvidia's Fermi GPUs are crippled in DP performance to a quarter of their potential. The Tesla or Quadro GPUs with full compute capability are not yet launched and will have specs inferior to the GTX470 (GTX480: 1400MHz,480 shaders, 215W; GTX470: 1200MHz, 448 shaders, Tesla: 1150MHz, 448 shaders, 249W).
The Tesla should perform less than a 5850 in gaming apps, and use far more power, and AMD/Nvidia's professional graphics card drivers do indeed have much lower gaming performance than their desktop cards (in return for higher workstation app performance).
So:
For gaming, buy a 5870 like you were going to.
For workstation apps (rendering), buy an AMD FirePro [tend to be better value than Quadro, and Nvidia has yet to produce Fermi Quadros].
For GPGPU apps (Photoshop), buy a Quadro/Tesla.
Seems you need three cards, not one.