Since it's only single band, what band am I getting out of it? 2.4 or 5ghz?
2.4 GHz signals are quite a bit stronger than 5 GHz, so unless you literally have line-of-sight between the AirPosts, the 2nd Gen is picking up the 2.4 GHz signal and extending that.
Maybe I'll try a new Express to utilize as an extender since it's both bands simultaneously or a used 5th gen.
The big downside to extending using wireless is that even with a very good connection between the AirPorts, you will typically lose about half of the potential speed on the entire network. So, at best extending using wireless is a real compromise.
A no compromise setup would be two new AirPort Extremes, both connected together using an Ethernet cable. There is no speed loss on the network when you do it this way.
A new Express has only 100 Mbps Ethernet ports, so if you try an Express instead of a new Extreme, the maximum speed that it will allow is 100 Mbps over either wired or wireless connections. That's a loss of 900 Mbps compared to the AirPort Extreme.