Good question. Off the top of my head: 1) much better wireless performance, higher modulation at lower receive signal levels. 2) easier channel planning - you use the same channels across all your towers and the core figures it all out. 3) you can potentially get roaming agreements with carriers (I don't know of anyone who has successfully done this but apparently it's feasible)
Big disadvantage is cost - you have to run a core which is very expensive ($100k+) Or you can use BaiCells and they'll rent you use of their core for fairly cheap.
I would very much recommend against this - off-the-shelf core networks are shit. Look up "SS7 vulnerabilities" on Google to see what I mean... and yeah your LTE core network would be based on that.
LTE itself is good but you'd need to build a proper core network for it - at the moment none of the off-the-shelf gear you can buy is any good.
