Ilevel sync caps the stat bonuses given by a piece of gear to that ilevel's stat max for that slot.

To work with your example, a BLM wearing the i250 Star Velvet Himation of Casting HQ (143 Vit, 144 Int, 82 Crit, 113 Det), a BLM wearing the i120 Demon Robe of Casting (47 Vit, 45 Int, 31 Crit, 31 Det) and a BLM wearing the i110 Evenstar Coat (41 Vit, 39 Int, 29 Crit, 29 Det) are all running the same piece of content with an ilevel sync of i110.

i110 caps for caster body slot gear are 41 Vit, 39 Int, 41 Crit/Acc/Spellspeed, 29 Det.

The Star Velvet Himation will sync to 41 Vit, 39 Int, 41 Crit, 29 Det.
The Demon Robe will sync to 41 Vit, 39 Int, 31 Crit, 29 Det.
The Evenstar Coat give 41 Vit, 39 Int, 29 Crit, 29 Det.

So the player in i250 gear will get more from their gear than a player in i110 gear when in i110 sync content.