Which 3S Lipo should I get??

My Mamba Max 5700 came in today. Once I get it installed in my XXX-T and play with it for a few days I am going to order a 3S Lipo battery. Is there any advantage, besides longer run times, in going with a more expensive 8000mah or 6000mah 3s2p over a much less expensive 4000hv 3s? I also want to make sure that it will fit in the battery tray of my XXX-T. All of them will probably be to big to use the stock strap so I will have to rig something up with some velcro or zip ties. I just don't want to spend $$$ on a battery only to find out that I should have just gotten something better in the first place.Thanks for the help you guys are a wealth of brusless/Lipo knowledge!!!