I have this stroller.... and love it
Amazon.com: Pet Gear AT3 Generation 2 All-...
This one has foam tires. My stroller is very good for bumpy-ish terrain. I took my girls to a dog show outside in it and it navigated beautifully. I'd say between air tires and foam, it's about the same. I think the size of the tires is most important.
Con of foam: some rocks get stuck in the tire.
Con of air tire: you have to fill them and they could pop.
If you have any questions about the stroller I have I'd be happy to help!