Will a french-link bit be more difficult for my horse to pull against

I used a french-link eggbutt snaffle for a long time with decent results. My trainer recently had me switch to a full-cheek. When I purchased my full-cheek, it was not a french-link. Now, I seem to think there have been a few instances where he's put the it in his teeth to disable my ability to control him well. Once, in the field, he avoided my asking him to slow down at the canter. He got faster and faster, and then we were galloping. As I pulled on the reins, his neck just got more stiff. It was like pulling against a tree. He did stop before going too far, but I think it was his decision. Not because my efforts were effective. Now, I'm wondering if a french-link would have made it more difficult for him to put the bit in his teeth. Does anyone know?

Ask your trainer to explain the different actions these two bits have on the horse's mouth and why they wanted you to switch.

The french link doesn't have the nutcracker action of a single jointed snaffle and therefore may be a good choice for horses with a low palate. Instead, the mouthpiece lays flat across the tongue. There is a lot more mobility within the mouthpiece, and so, some horses that may get "set" in a single jointed or mullen-mouthed bit, may go lighter and lean on the bit less in the French Link.

The full cheek snaffle uses a nutcracker action and the cheek pieces can be helpful in refining the turning aids and for preventing the bit from being pulled through the mouth. The keepers, by fixing the bit in alignment with the cheekpieces of the bridle, also add a small degree of pressure on the poll when the rein is used.