I have PTG , Brownells and a Wheeler..... they each fit slightly different upper "types".
YMMV,
The PTG ( Pacific Tool and Gauge ) fits most all AR15 uppers great and is my goto lapping tool. ..but, that is provided the upper isn't a thermal fit upper.
The Brownells fits "thermal fit" ( Like a BCM / SOLGW ) uppers perfectly .... The PTG won't even fit into a BCM thermal fit upper, the Brownells does.
The Wheeler one I tried, was such a poor fit on any of my upper brands... it now serves a internal buffer tube polisher.
FWIW... I don't put the upper into a vise, Imho, it is to easy to induce a slight off center pressure when it is in a vice. ( Well, it is for my typical "Bigger Hammer" mentality )
I prefer to lap the upper vertically and while everything is hand held. Oil the shank adequately and don't lap at the highest speed, let the drill do the work... don't force the upper onto the tools face to speed up the lapping.
Hand holding the upper to the lapping tool, for me, makes it easier to feel what is going on.
If you are lapping the receiver face.. consider shimming or Loctiting the barrels RE in place.