The historical impact of crossbows versus guns boils down to two factors: guns penetrated metal armor better, and guns required less practice for accuracy. Both deliver comparable energy to flesh (and both dump that energy pretty efficiently).
The crossbow, in the real world, has a reload speed limited by the wielder's strength. D&D5 ignores this.
The firearm, in the real world, has a reload speed limited by the wielder's manual dexterity and overall agility. Both of which roll into Dex in D&D 5.
So, in the real world, the best crossbowmen were both dexterous and strong, while the best musket-men† were simply dexterous. Both require taking the weapon off posture to reload, both have a multi-step reload.
The muskets, tho', pretty typically run about 2-3x the energy on the projectile. And concentrate it on about 1.5x the surface, for about 1.3 to 2x the penetration versus armor...
But the best energy is on very light quarrels - about 1 oz - and in the era of wood quarrels, that means pretty weak woods - balsa, willow - which don't have good arrow qualities, and will shed energy on shattering if not a good hit.
D&D doesn't model armor penetration well - and the energy dump is often lower with musket, because the ball is more likely to go through the target. we're talking crossbows in the 60-100 foot pound range, and .60 cal muskets in the 150 to 400 foot-pound range. Oh, and the wearing of breast and back plates made muskets WORSE... because they usually dumped enough going through the first time to bounce off the opposite armor, and back in.
You can easily justify increased damage for firearms as a move towards realism.
No other changes are needed - the lack of granularity is going to make any difference other than what you need for loading rather moot. The ranges should even be comparable. The price for early ammunition and powder is high - the materials aren't that rare, but are in much demand for other things, and making powder is dangerous, smelly, and unpleasant work.
Making crossbow bolts is skilled labor...but really, about half as long per bolt as making powder.
So, powder per shot, probably double. Bullets, cheap - same as sling - but higher quality preferred. Damage, up a die to two.
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†properly musketeers, but that term's baggage laden in english.