Leveling dungeons (1-49, 51-59, 61-69, 71-79) are synced almost to the minimum item level that the content was tuned for, so everything hits really hard. There is a gear progression but once you are in gear from a few levels higher, it's already being synced.

Max level dungeons (50, 60, 70, 80) are often Item Level synced (there is an icon next to the dungeons that are). It will say in the details what item level the enemies are scaled to (average item level) and the item level it syncs to next to it. If it's not item level synced, then it syncs to the maximum item level of the expansion.

The maximum item level for each expansion is...
50 (130)
60 (270)
70 (400)
80 (530)

8-person content is always synced to the maximum item level of the expansion, so at level 50 this is 130. This is often double the item level the content is tuned for, making it extremely boring compared to when it released.

If you have a pre-formed party you can use the Minimum IL and Silence Echo settings to make it more fun or challenging.

Materia doesn't count when you sync down. The difference in a sword that is higher than the sync is what stats it has on it, but not the amount of those stats.

Something that doesn't seem to sync well is food. If you use level 80 high quality food, you will be a lot stronger than if you use level 50 high quality food.

FATEs only level sync you, but like with leveling dungeons, if you sync to 57 in a 52 FATE your damage will still be low because that is a difference between 130 and 142, but if you sync to level 60 in a level 55 FATE you will destroy it because the difference is 136 and 270.