I'm looking at purchasing SAE and Metric sets of combination wrenches with an open end on one end and ratcheting end on the other.

I see some sets have a swiveling ratchet head. Is there any advantage to having the swivel head? Do you not have a problem with the swivel head flopping around when you try to use it?

 

Yes. One with a swiveling head may in certain conditions be useable where a straght one is not.

Get the type with a screw with which the swiveling head can be fixed to a certain position (or the "flopping around" decreased). In very tight spaces a non-moving (but angled) head may make the difference between being able to apply the wrench or not. Those without such a screw will invariably become too loose with time and make attaching the ratchet onto the screw head in tight spaces more difficult.