Parallel Batteries

"Is there any drawback to having 4 GCB's in a series parallel configuration as opposed to 2 bigger L16s in series?"

(I am assuming that GCB's stands for Golf Cart Batteries, typically 220 amp hours at 6 volts, and the L16's as 350 amp hours at 6 volts as opposed to the L16 HC's which are 400 amp hours at 6 volts.)

Otherwise, all things being equal, possibly, the only "drawbacks" I would have would be; GCB's - footprint, more holes to put water in, fewer cycles. L16's -  less amp hour capacity, higher cost. But then again, where true deep cycle flooded cell lead acid batteries are concerned, there is no equal ground is there? I mean, its a free for all amoung manufactures and how they advertise.

"If I go with the 4 GCBs is it acceptable to put a 125A breaker off each series pair.  Or do they need to be paralleled first and sent through a 250A breaker?"

I am not sure I comprehend this one as you would have me understand it, but I will go with what I believe is your intent.
 Two scenarios;
First - 4 GCB's, 2 pair, each pair wired in series but the 2 pair are not wired in parallel. Instead, 2 sets of wire are paralleled from each of the 2 pair of GCB's to the inverter.

Don't expect any prizes for original ideas from this set up, but do expect some suprises and added inefficiencies from it, if its not done just right. Paralleling wires to a load can get tricky. But hey, if you've already got the stuff to do it and your confident in your skills, go for it. What have you got to loose?

Second - 4 GCB's wired 2 pair in series and those 2 pair wired together in parallel with 1 set of properly sized wires going to the inverter.

Ahh! Now theres a smart man. Simple. One breaker to deal with.