On the Kodiak, and I assume there's something similar on the Springbar, there are vents at the top of the side walls (the green triangular flaps you see in pics). This is on the deluxe/typical models. The Basic version does not have vents. I haven't taken mine out on a super hot and humid trip, but it did well in the warm weather.
I don't have experience with the REI and Big Agnes. I'm sure they're great. I think it really comes down to whether you want a canvas tent or nylon tent. My Kodiak is strictly for car camping, so weight wasn't an issue. With a family of 5, I'd go for the bigger 10x14. 10x10 may work, but I'd prefer the extra space.
As for Springbar vs Kodiak - they're both great. I would have been willing to pay a little extra for the US made Springbar, but they had a 6 week wait at the time. But I actually like some of the features of the Kodiak better.
95 FZJ 80
07 BMW XChallenge
05 V-Strom 1000