In 2E it was because they were a better magic user for most of the game. For example level 4 bard and level 3 mage required the same xp and had the same spell pattern and Bards had this up to level 16 or so IIRC.
That's not at all accurate. Here's a breakdown:
Starting out at 0 XP, the wizard knows a few spells and has a spell slot - the bard knows zero spells and has zero spell slots (sure, he picks up a spell slot at half as many XP as the wizard needs to get a second slot, but there is zero guarantee of having any spells to cast it with, and the bard doesn't even get
read magic as guaranteed so they could fail a learn chance and not even be able to use scrolls to learn new spells).
When the Wizard reaches level 2, the bard is level 3 - they have the same spell slots, but the wizard is guaranteed to know a few spells and the bard isn't (and that's reiterated enough, so I'll stop mentioning it now).
When the Wizard reaches level 3, the bard is level 4 - they have the same spell slots.
When the Wizard reaches level 4, the bard is level 5 - but from this point forward the wizard always has more numerous spell slots of at least one spell level
When the Wizard reaches level 5, the bard is level 6 - but from this point forward the wizard not only always has more numerous spell slots, but has higher level spell slots too.
The only thing which might make the bard be considered "better" is all of the parts of the class that
aren't spellcasting, because the bard has a number of such features which is greater than the zero the wizard has, unless they are a specialist in which case their ability to cast spells is even more potent than the bard because all the above XP values where I've said the spell slots are the same the wizard actually has more than the bard, plus better learn chance and a save penalty for the favored type of spells.