In order of decreasing significance:

1. 5E spell slots don’t have their usage decided when they’re recovered.
2. 5E spellcasters have certain capabilities which are inexhaustible and mechanically significant enough to displace mundane capabilities (some of these are rituals, but most are cantrips, with attack cantrips displacing missile weapons; the light spell displacing use of torches, lamps, and lanterns; and various utility effects such as mending, message, mage hand, dancing lights, and minor illusion which tend to devalue various mundane capabilities or even other magical capabilities – unseen servant is worth less when mage hand is available at-will, and the same goes for silent image vs minor illusion).
3. 5E saving throws are dependent on the caster rather than the target and can improve over advancement faster than a target’s ability to resist.
4. In 5E, spellcasting cannot generally be interrupted or otherwise prevented.
5. In 1E, a number of spell parameters scale automatically with the caster’s level (range, duration, damage, etc.) while others don’t scale at all. In 5E, only cantrips scale for free; some spells can be made to scale by casting them with higher-level spell slots, but only in specific ways. Some spells can be scaled by this which don’t scale in 1E (e.g. Sleep).
6. In 5E spellcasting abilities combines across levels in different classes; in 1E they’re totally independent.
7. Spells in 5E generally don’t impose on the beneficiaries any costs (like aging) or risks (like system shock rolls or chances of insanity or the ire of lower-planar beings).
8. 5E spellcasters have no critical factors that can compromise their ability to use magic – the favor of a patron deity for clerical magic, access to a spellbook for Wizards/Magic-Users.
9. Most limitations on 5E spellcasting classes purely indicate a lack of training (Wizard inability to cast spells in armor, limited selection of weapons for Clerics) rather than an actual limitation on what they can do

This is in addition to the effects of differences in individual spell definitions (concentration duration, ability to create long-lasting effects via repeated castings, and weirdly-redefined spells like Leomund’s Tiny Hut).