Hey zapy85. I tested on two games, Battlefield 1 and Battlefield 4. Interestingly, there's no FPS difference in BF1, but in BF4 it's easily reproducible. The easiest method is simply spawning into the test range and taking note of the FPS. I used MSI Afterburner to record the average, but of course the game engine's FPS counter will do if you don't use that.
Using Origin the average FPS was 673.
Using EA Desktop the average FPS was 572.
Obviously at such high frames it wouldn't really be noticeable, but the fact a 15% reduction in performance exists shouldn't be happening.
I have the in-game overlay disabled in both programs just in case that was affecting it.