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?
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.
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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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.