I have both types of pads. The plus for the thermarest is speed & convenience. The BA is cushier but if I'm on a trip where I'm packing up every day I get tired of inflating and deflating. If I'm going on a long tour and moving on every day I take the thermarest. If I'm going to be camped in one place for awhile I take the BA.I have hear a few people who say this so I guess maybe I am in the minority on this one, but... I don't get it.
I have the medium sized NeoAir (same thickness as the Big Agnes) and it takes 15 breaths to fill it. It takes maybe a minute, two minutes tops. Really not a big deal especially since the Prolite 4 takes a few breaths even though it is self inflating. The added ease of rolling it up makes up for any extra effort in inflating for me.
To me there are only two downsides to the NeoAir. The first is cost, which is pretty high. The second is that the R value is a bit too low for winter camping.