An underpinner itself doesn't take up much space, as you likely know, but the work are can be large depending on the frame.
I think this is true with Thumbnailers.
I prefer an underpinner, and have only used older AMP models.
I have experience with a used Hoffman, and it is quite useful for tall thin moulding, such as Floater Frames, and Shadowbox frames.
I think my main preference for the underpinner is when fixing something done wrong.
If a frame is mis-made, and assembled with underpins, carefully break apart the frame (a challenge), make any changes needed to the frame, and re glue and nail.
If a frame is mis-made with a Thumbnailer, shaving the frame down a bit may make it impossible to reattach with thumbnails.
I have had to refame a few things where the routed channels did not line up in the corner. This often meant that they just left the Thumbnail out and glued where the limited bits of wood were. This could also mean that the frame is misaligned in order to line up the Thumbnails.
This is not to blame the machine, but the operator.
I think it is easier to do a good job with an underpinner.