Congrats on getting a chinchilla.
The second cage is better. The first one is too small and has a lot of plastic parts. Any plastic exposed to a chin usually gets chewed on and destroyed. Ingested plastic is potentially dangerous to any rodent so that should be prevented.
Chinchillas like to jump from shelf to shelf inside the cage and like vertical space. If you get the second one (Critter nation) do not use the wire ramps as these are notoriously dangerous for chins. I had a chin come close to being injured by jumping on top of a wire cage when his foot went between the bars and he slipped off the edge. It easily could have resulted in a fracture but thankfully it did not. The same can happen with these ramps. They don't need them anyway.
Although I don't have this particular cage I know some of our regulars do. They say it has a plastic tray. An aftermarket custom made tray can be ordered online if you find it's getting chewed up. You might also consider ordering sheet metal or wooden guards that keep bedding from getting scattered too far since the trays are shallow and chinchillas are very active animals. At the least you might want to be prepared to use a rubber mat if it's over carpet.