OK. Let me try, and then everyone can say how wrong I am. Wargames involve losses--people killed, wounded, ran away or whatever. We need to keep track of them. We also need to know who's fighting who--what units are involved--and we need to know what sort of troops are fighting--massed units, skirmishers or whatever. Depending on the rules, basing gets involved in all three of those.
Start with casualties. You can either keep track of all losses with tokens or paper, keep track of them by removing entire bases, keep track by marking certain castings on a stand as "dead" or--and yes, I've seen it done--some combination of those. Different numbers of figures on a base can really mess up keeping track of individual losses.
Keeping track of who's fighting who is less of a hassle--as long as everyone is using the same basing. But the choice of basing limits you to opponents who base the same way. If your bases have a frontage of 1" and your opponent has different frontages depending on the number of men in his regiment, which would be normal for the Johnny Reb series in the ACW, for instance--well you can see the problems. There are also tactical problems if the rules assume 100 men occupy a 1" base on the table, and now those 100 men occupy a 2" base. Other distances would need to be adjusted or you get some tactical distortions.
And there are rules like the DBA series which use the number of castings on the stand to keep track of what sort of unit it is, so if you don't abide by the conventions of those rules, you drive everyone else nuts.
Those are practical problems. But it's a visual hobby, so there are aesthetic ones as well. People complain about the "Empire" series where the very small units in single rank look more like color guards than battalions. I myself have grumbled that the very common 4 castings on a 1" base often used in 15mm ACW rules looks like a four-rank deep line (not seen since the 18th Century) if I use such castings in F&F Regimental. The game would still play, you understand: it's the appearance I object to. But if appearance didn't matter to us, presumably we'd be using cardboard counters--or computers.
So the answer is IF
1) both armies use the same frontage bases,
2) all bases of the same troop type represent the same number of men in the same formation, and
3) either it's the same base width the rules are written for, or other distances have been altered to correspond
Then it doesn't matter for gaming purposes. The appearance may matter to you or your opponent--or may not.
But a lot of times those three conditions aren't met.