The two big difference between D&D 3e and AD&D 2e for spellcasters was saving throws, and volume.
In 3e, your saving throw goes up with level (fast for some saves, slow for others). The wizards DC also goes up (with spell level, and their stat).
In practice, the DC goes up at a speed matching, or exceeding, the good saving throw of the target, when using top-level spells, and the DC growth matches or exceeds the poor saving throws of the target when using even their lowest level spells.
This means that at higher levels, targeting a poor save with a medium-high level spell has a higher chance of success than you had at low levels.
In AD&D 2e, the saving throws of individual foes (be they dragons or fighters) got uniformly better. The chance of landing a spell decreased. There was little you could do (and nothing happened automatically) to aid in landing a spell.
In both 3e and 2e, higher level spells had worse consequences. But in 3e, they where also (in practice) easier to land against challenging foes.
The math in 2e was that probability of landing the spell, times consequences, did not climb that fast (if at all) for save-or-suck style spells.
Spells that had effect even on a failed save, or did not require a save, thus became more powerful. Most of such spells are damage spells: they interact with a foe by the same mechanic that fighters do (lower the target's HP).
The other big effect was volume. 3e imported most of the 2e spells, rewriting them for 3e (with the better success chance, higher number of spells per level, easier wands and scrolls, etc) often without reducing their power. Then even more spells where written.
Each time a new spell arrives, there is a chance that a constraint is removed off the wizard. Maybe there are no good save-or-lose reflex based spells in the game: then a spell that wraps the target in a cocoon is added on a failed reflex save, and now targets with weak reflex can now be taken out by the wizard on a single failed save.
Metamagic, increased spells/day, ease of creating magic items that boost spellcasters (wands and scrolls), ability to plunder every monster manual for stats on some spells & monsters scaling faster than "naked" fighters: these are all just icing on the cake.