Full Length and Small Base are both "full length" sizing dies.
I recommend Small Base for any gas guns because of the powerful extraction forces involved. Small Base will "size", particularly down towards the base where it matters, a case down closer to its true unfired dimensions. I think Small Base dies are probably just a little tighter tolerance, so they get sold as such, but I do think it helps in terms of preventing stuck cases.
A competition die just gives you finer adjustments in terms of bullet seating, for the most part. Unless you are really "geeky" in terms of these things, (I admit I am) it probably wont do much. It does provide a more precise means when seating long bullets (like 80 grainers) based on distance off the lands...
Keep in mind though, not all dies are equal, thus not all small base dies are equal. I pretty much only use Redding, so I dont know how much the tolerances differ in other brands. Also, any of the Redding Comp Dies will probably require bushings as well. The good ones are about $20 a pop. Make sure you know what you want and get two more + and - the size you decide on, just for some margin of error or different brand cases...