My understanding is that to do the same SSID on 2.4Ghz and 5Ghz and have your devices connect to the correct channel based on their capabilities, your router needs to support "smart-connect" or Tri-band. Without this, your devices won't be automatically switched away from the 2.4Ghz channel to the 5Ghz channel if they support it.

I'm not sure if you can accomplish smart-connect / Tri-band with two separate routers, I would suspect not.

I think Matt's right - you need an access point capable of managing its clients across the two bands. I've used a few Ubiquiti AP's and they seem to manage it pretty well, for example.