Just get a 5770. The 5870 offers little benefit in the 1,1. Performance ceiling of sorts. can't say if it is just because of procs or if it is a limit on the board. Which would also mean a 6870 would suffer the same as it is a slower 5870. More or less.
The PCIe lanes are generation 1.0 for all slots in the 1,1 and 2,1 systems IIRC, which would throttle a fast enough GPU card.
What else would there be available with the flashed EFI?
The ability to add future graphics cards.
Right now, ATI's cards work as it uses EBC firmware, which works in both EFI32 and EFI64 systems. So adding a current ATI card isn't an issue.
Where it will become one however, is once OS X shifts to a 64 bit Kernel
only (aka K64), the drivers won't be updated for those stuck using an older copy of OS X due to the necessitation of running K32, which would be all 1,1 and 2,1 users.
...flashing the Mac Pro's EFI - be it to the 2,1 EFI or a 64-bit EFI (which I now know is more-or-less impossible).
Unfortunately, it is for all intents and purposes (not something the avg. computer user, even when computer literate would be capable of).
I inferred that newer cards (like the 6870) could only be fully utilized with a 64-bit EFI. After this thread, it sounds like that may be true. However, since the 1,1 and 2,1 EFIs cannot be flashed to 64-bit, there seems no reason to throw the extra $70 from a 5770 to the 6870.
No, there really isn't. You'd get a marginal performance increase, but not what the GPU is actually capable of generating.
As per why, see above.