Baze of Bahamut |
If crit range were not an issue, the only difference would be most likely damage outcome. A weapon dealing 1d8 would be much more likely to roll max damage than a weapon that deals 2d4, however the 1d8 weapon has a minimum damage of 1 (not including any bonuses to anything else), whereas the 2d4 weapons minimum damage output is 2.
For example, I made for a short sandbox one-shot campaign I helped run a weapon that deals 4d2 damage, with a crit range of 15-20. On a crit (which occur 30% of the time), it would deal anywhere from 8 to 16 damage, but the majority of the time it would deal 12 damage, give or take 1 point.
Whereas a 1d8 weapon, on a crit, has a much higher likelyhood of deal 16 damage on a crit, but can also deal 2 damage on a crit.
More dice just increases the likelyhood the final weapon damage will land in the middle of the damage range.
That said, House Rule for me and the DMs I usually play with is a nat 20 is a crit no matter what (none of the junk about confirming it). Increased crit range will crit if the roll also hits the target's AC. So with the above mentioned weapon, it could crit and still not hit the target's AC.