I like egg buts because the head stall holds the bit at the correct angle in their mouth, more so than loose rings, but not so much as a full cheek with keepers. D's and Eggbutts and Full cheeks also provide a good deal of lateral movement, so when you pull one rein it applies pressure on the outside of the mouth on the opposite side. So pushing the mouth over as well as applying pressure to the tongue/bar.
Personally I prefer french link over single linked bits, simply because it reduces the nut-cracker action. But some horses don't like all the mess of the two links and do better in a single joint. Tends to be horses with a low pallet wont like single jointed. You could also try unjointed, mullened out mouthpiece, I like them.