I own both a TT 3-day and an SOB THE pack, and would recommend either without any reservation. I've read several posts by guys over at LF.com complaining about the SOB shoulder straps, but I've had no problems with them ('course I'm not quite Eggroll big).
I like the multiple pocket design integral to the SOB pack (two zippered outside, one mesh zippered inside), but the simplicity of the TT combined with the PALS gives you plenty of options. If you want PALS, the SOB and RAID are about equal in the amount available. The shoulder straps on the TT are much more thickly padded than many assault packs out there, which can be nice if you're hauling around more weight all day. I don't have an Eagle A-III, but have fingered one or two and they're very well built, but lack any PALS if you're wanting modularity. The RAID is also an excellent pack, but as has been said availability can be spotty, and its the most expensive of all you've listed.