While either way, you need the pretty much the exact same chip, what you will need to do depends on if you are replacing the CMOS RAM chip or the Flash BIOS ROM IC.
The Flash ROM holds the actual BIOS code. Without the correct BIOS in the Flash ROM, you will not be able to boot your computer and load the bios into the flash ROM. You will either need a programming station for the Flash ROM, or you must purchase a Flash ROM that has been pre-loaded with the specific BIOS for your motherboard.
Now, if it is the CMOS RAM chip, while it still needs to be the same size and speed, there should be no problem replacing it with a chip made by a different manufacture.
In the case of replacing the CMOS RAM, your motherboard will power up the same way it would if you were to reset the CMOS. You will need to enter BIOS Setup and set or at least verify all of the settings.
Back to your base question:
Flash ROM:
Same manufacture, same series, speed and amount of ROM are required. Minor differences in revision should not be a problem.
CMOS RAM:
Must be same speed and same amount of RAM. While nearly any manufactures part should work, there may be some CMOS RAM chips that will not work properly with the BIOS Flash ROM. It would be best to get the same manufactures part.
I am very curious as to what kind of failure you tracked down to either the CMOS or the Flash memory IC. I would expect many other things to fail long before either of these devices would fail.
Chas