My eventer and foxhunter are both in Korsteel french link eggbutts. The eventer occasionally goes in a Pessoa gag (commonly called elevators) with the primary rein on the snaffle and a curb rein on the next ring.
My reiner is happiest in a medium-port, medium-shank correction bit.
My Arab colt likes a single-jointed loose ring.
My mom's Percheron (trail horse) is in a Myler Dee ring, single joint with lots of tongue relief.
My Paso Fino (trail horse) is in a Brenda Imus Easy-Gaited bit.
My brat goes best in a french link full cheek. And recently discovered she HATES flash nosebands. I lost my flash so was riding her all winter without it and she was a dream. I put one on a few weeks ago and she has been a brat. So I took it off and she went back to being a doll. The funny thing is, I never adjusted it tight.
So yep my jumper/eventer likes just a simple full cheek french link and lightly adjusted noseband. Might be getting a kineton noseband for cross country. Still debating.