#1
How important are the physical speakers (i.e. Celestion) in your physical cab when using Effects Processor Amp Modelers like the Axe-FX, Kemper or Boss GT-10?

I am paranoid that I could be getting dramatically better tone output if I were to buy a more expensive cab with better speakers.

I have a Marshall MG250DFX that I use strictly as a 2x12 cab with my Boss GT-10 as the preamp. Would I see a dramatic improvement in tone if I bought a $750 cab with "better" speakers?
#2
Depends. If you're using the cab sims on the Boss, having any kind of guitar cab would be detrimental and you'd be better with a full range speaker or PA system. If you're just using the pres, then yes, a better cab will always be an improvement.
Depending on the amp model, different cabs will be better. For example in Marshall world, if you're using a Plexi or JTM, a Greenback 25 loaded 4x12 sounds great, whereas JCMs and JVMs sound great with V30 loaded cabs.

It all comes down to preference.
#4
If you use cab simulation on your amp sim then a better FRFR (PA) system will make you sound better.

If you don't, then a better guitar cab will make you sound better.

Everything will be better than what you're using now really.
Name's Luca.

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#5
I have a peavey 6505+ head, and I used to have a cab that wasn't all that great. The tone suffered a lot. I bought a new cab with decent speakers and let me tell you that it's deff worth it man.