Have I misunderstood the Verizon unlimited plan

The "value" of T-Mobile depends on where you travel. Although they are expanding their network, their 4G coverage area is still much less than Verizon's.

I had their service (in addition to a Verizon plan) last year at an RV park in FL where we winter and dropped it after a couple of months.

Although T-Mobile had decent service in that FL town, service when traveling away from towns off the interstate was spotty at best.