There are quite a few places where I have seen consistently high latency on Verizon's network one of which would be here in Cleveland. Latency sits around 125ms+ and speeds never really surpass 12/3 Mbit/s. It's about as bad as using 3G to browse the web. Even though you have good download speeds you still have high latency which makes web browsing feel sluggish. If Sprint can one up Verizon here I wouldn't be surprised. Clearwire WiMAX is already better than Verizon LTE here. Sprint seems to have consistently low latency all around the country with very little variation.
What does a traceroute look like out of CLE? I know that for awhile Verizon was hauling LTE traffic in Denver out to Seattle before doing anything useful with it. I imagine that the issue is similar where you are.
T-Mobile is actually quite good about this, as is CricKet; since neither have national backbone networks, they'll just dump traffic onto the Internet at the nearest large city.
I can't check on Verizon right now, as my mom is the one with Verizon LTE and getting her phone from her for 5 seconds to run a traceroute will be like pulling teeth, but I can try and grab one later on today.
I wouldn't doubt Verizon is doing something ridiculous with traffic before it hits the internet from here. Verizon shouldn't have any problems putting in a LTE core here. Sprint has managed to do it just fine, eHRPD is already up and running in CLE.
It seems like everything from CLE on Sprint's network goes to CAK and gets dumped onto the internet. Latency from CLE to CAK is ~5ms on my home internet (it should be much lower for fiber). This should mean that latency on Sprint's LTE should sit around 25-30ms for local sites and 35-50ms for everything from the east coast to Kansas.