Which makes the bigger difference?

Agree with Michael.

I would look into Audio Research tube pre and SS Amp combo. See if anyone else with Apogee speakers are using AR gear.

My experience is that anything that obscures low level detail will reduce soundstaging. After all, it is the low level detail that creates the soundstaging effect. All components in a system will obscure detail to some extent, so more revealing gear all around will improve soundstaging.

Another crucial aspect is vibration control. If you are using the stock rubber feet that come on most gear, this will obscure low level detail. Switching to cones and other such footers will make a big difference.

gotta agree with the speaker-room guys

Given your speaker setup is as good as possible... and so forth... the biggest improvement in sound staging, and imaging results for me came by way of going to mono blocks. Tube or SS. First was SS twin mono's on one chassis. Super. that was followed by actual separate twin mono block tube amps. Better in many ways, but they don't match the presence the big dual mono stereo SS amp provided.

Each instance was channeled thru one of two tube preamps in SE fashion. Although the tube monos don't provide the immediacy of the SS amps, nor the bass impact, I do enjoy them equally well... and I am continually torn between the two distinctly different sounds each presents.

the best situation? having both tuype amps is clearly the way for me... and just switching back and forth from time to time as the mood indicates.

having both available, I am not intrigued sufficiently to bi amp my speakers with them either.