In the course I teach at a local community college, I have my students conduct a lab to prove the fact that the two access points should be on the same channel. The reason is that 802.11 uses CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance). Briefly, this means that one access point won’t transmit when the other access point is in use. Why is this better than operating on two different channels? Because, in the real world, two access points in the same close environment create some RF interference for each other – even if their frequencies are separated as much as possible (in the USA, the greatest possible separation would be to use channels 1 and 11).
Your description puts the two APs in the same, essentially open, area. If the two signal strengths are dramatically different – say, a signal from another business next door that is 30 dB below your signal level – then yes, the use of two separate channels is appropriate. But in one overlapping area with approximately equal signal levels, use of the same channel provides both maximum coverage and throughput. Please note that the throughput of two overlapping APs on the same channel won’t be as good as the throughput on a single, non-overlapped AP. But it will be better than the throughput of an AP that is experiencing harmful interference.