There are several advantages of fixed clamps:
Job Quality - The strings won't lose as much tension. Fixed clamps are anchored to a solid base, so they move less. Also, when you work with strings that are far apart, like the outermost strings, you won't lose tension because you don't have to squeeze the strings together.
Versatility - One-piece and ATW patterns are much easier with fixed clamps. Certain other techniques, like JET, require either fixed clamps or special tools like triple floating clamps. You can still keep your floating clamps and use them on a fixed clamp machine when you need extra clamps, but you can't use fixed clamps on a floating clamp machine.
Speed and Convenience - They are easier and quicker to use, but honestly, that's the least of their benefits.
I agree that Gamma and Alpha have great entry level fixed clamp machines.