Are the chain tensioners on the All City dropouts a big advantage?

They're convenient to have but not a necessity, tensioning your chain on a FG/SS bike is pretty easy without them. Just pull the rear wheel back with non drive side of the wheel touching the NDS chainstay and tighten the NDS track bolt. Use your hand to push wheel toward DS to modulate tension while/ holding it when you tighten DS track bolt. Loosen NDS track bolt so wheel centers itself and retighten.

Any big difference between 620 chromoly and Reynolds 725 tubing?

You mean 612* for the all city. There's not much difference aside from the reynolds being branded and probably the quality tied in with the brand. But this shouldn't be too much of a deciding factor considering both are double butted chromoly.

Bottom Bracket drop is 58mm on the All City and 62mm on the Wabi, Is this a significant difference?

From a geometry prospective, a higher BB is more suited for track riding/ geometry. Although a lower BB is preferred for a less aggressive/ comfortable/ casual ride. It really comes down to you deciding/ your tastes for crank length and working with that.

If you own either of these bikes: What do you like about them? Anything you do not like about them?

There's owners of both here. They should be chiming in soon.