They're not that "out of sync". T-Mobile has a decent amount of Band 2 (PCS) spectrum thanks to their MetroPCS acquisiion, and in many markets they have either 10x10, 15x15, or 20x20 band 2 LTE deployed. Sprint's primary / base LTE band is also PCS, and is band 25, where they have at minimum 5x5 deployed (some markets have a 10x10, some have 2 5x5s, and others have both a 5x5 and 10x10. Band 25 is a superset of band 2.
So for current Sprint customers, nothing would be needed to start using T-Mobile's band 2 LTE. I think a decent number of Sprint devices also support band 4.
Going the other way, it might be more difficult for T-mobile customers to use Sprint's infrastructure without new handsets. Some will be able to use band 25. At the very least, they could likely move the CDMA carriers within their combined PCS spectrum and expand B2 bandwidth.
Devices like Nexus / Pixels and iPhones (excluding the T-mobile variant of the iPhone 7, Sprint's version is fine) will work with either carrier. Google has been working on a "hybrid" network called Fi for a while.
The problem devices will likely be Samsung devices, since they remove support for a lot of bands and have very carrier specific versions.