Let's look at this in more detail.
- Magic-users have a d4 Hit Die, while elves have a d6.
- Magic-users are limited to daggers for weapons (although many people house-rule to let them use staves, per AD&D), and cannot wear any armor. Elves can use any weapon and wear any armor, although the latter would seem to prevent them from casting spells; the usual house-rule solution I've seen is to let them wear leather armor only.
- Elves also have infravision and an enhanced ability to detect secret doors.