600W only tells the maximum power output. It doesn't tell us whether it can support dual-video cards. The specific model would help. Ultimately, you need to make sure it at least has two PCI-E 6-pin power connectors to support two different video cards power wise. Also, the amperage on your 12V rails is important.
As far as your motherboard goes. Is this your board?
Others have already told you the news about SLI vs. Crossfire on the X38 chipset, but here are a couple more things to consider.
nVidia recommends at least a 700W PS for a dual SLI setup. If you plan to overclock, I'd go larger than that so you have plenty of headroom for fans and other goodies - and just because it's a good idea to have more power available than you need. No sense in stressing hardware to the limit. A PS rated at 900W and one rated at 700W will both deliver 700W to a system that only needs 700W, so a larger PS makes sense in that once you get past the up-front cost, both deliver the same power but one does it easily with room to grow and the other is close to maxing out. If you go with a 700-800W unit, make sure that it has four 6-pin PCIe connectors and that it delivers enough current on the 12v rails to support your video cards. Almost any new 900-1000W PS will meet your needs in that regard. Some of the larger power supplies are monsters though, so make sure your choice will fit your case.
Opinion: In my experience, the nVidia 680/780 chipsets are a bit harder to overclock than the Intel chipsets. It can definitely be done, but you may need to play around more to get your system stable at higher CPU speeds. They are the best answer for an SLI setup. Others may disagree, so I don't want to start a flame war here. It's just one guy's experience with a bunch of different boards.