There have been several studies that bridles affect range of motion of front and hind limbs, and breastplates can affect range of motion in the shoulder and jump trajectory. Both done by Fairfax – and while both are peddling a specific product, the studies themselves are peerviewed IIRC.
I feel my horses go better in a saddle pad with the sheepskin directly on their back, versus a plain regular saddle pad. No scientific data to prove this, just my personal feel when I ride them in different saddle pads.
I also think that bits affect ROM and tension as well. Again, no studies to prove this. Just noticing how most of my horses have a much more naturally collected canter when I am riding them in a halter or hackamore (non-mechanical). My one horse in particular, who is a superstar in dressage, really seems to be much more confident and collected in his body when I school dressage in the La Cense bridle - which is really just essentially a leather rope halter.