I'm leaning toward an 870 myself... I went and looked at a few different 870's, 590's, and 500's today, and they each seem to have their positives and negatives. To be honest, both seem pretty close in all aspects: comparable aftermarket parts and configurations, reliability, accuracy, government acceptance (police force with the 870, apparently USMC with the 590). I think both the 590 A1 and 870 tactical are roughly the same weight... in general the Mossbergs seem to be a bit lighter (the 500's at least), but I suspect the heavy barrel on the 590 might make up for that.
From what I've been told by the shops though, there is a slight difference in terms of "build style" in respect to intended use... it was suggested to me that the 870 may be geared a bit more towards reliability in the long run, providing you treat it right. The hardware is built to withstand abuse, but apparently the tolerances are a bit tighter, and it might be more prone to jamming in extreme conditions. The Mossy's are apparently "hunting camp" guns and are designed to be abused, with slightly looser fit in the action to allow for operation even when dropped, wet, and dirty. Then again, I've also been told that the Mossberg build quality is not quite as nice as the Remy's, and you might get 5-10 years before you start running into issues, as opposed to 12+ for the 870.
I'm aiming for an 870 myself because I'm looking at picking up a used basic one, cheap. I want to modify it and make it somewhat more tactical looking, although I've got certain parts in mind that aren't really available on any one particular "model" of 870. It makes more sense to me to buy the basic one and add parts as I see fit, rather than buy the more expensive "modded" one and replace parts anyway.