The signal being fed to the amps in your Summits comes from your amp through your speaker cables, so both the amp and the speaker cables will affect the sound of the bass produced. It's easy to understand that a powerful solid state amp feeding your Summits would send a signal that would produce deeper tighter bass than a lower powered tube amp would. The amps in your Summits amplify the signal they get and that signal would be different for each of the two types of amps mentioned above.
I don't know if the speaker cables will have a large or small effect on the bass, different people would probably disagree about this. The speaker cables would probably have a greater effect on the panels, so I would consider that matchup more important, but you never know.