Are you trying the same strings on the pinned and pinless type bridges, and are the scale lengths the same?
The reason I ask, is because tension=pitch, given the same weight of string, the part of the string in between the nut (or your finger) and where it passes over the saddle has to be at the same tension or the pitch will be different.
Less tension equals lower pitch. A greater break angle may give more tension after
the saddle, and thus down force, but this affects the energy transfer into the top, and thus tone. Not tension on the part of the string you play. I won't go into tone, as it's all subjective anyway.
Ways to get the same pitch with less tension are confined to lighter strings, or a shorter scale length.
I had this friendly argument with a semi famous guitarist I used to tech/roadie for. He played a Les Paul, and insisted I string the tuno matic bridge from the front, bringing the strings up and over the top of the tailpiece instead of through from the back. He swore it gave 'less tension'....I actually drove myself nuts with the physics of it all, but it actually made no difference to the tension once it was tuned to the same pitch.
If you prefer pinless bridges, go for it!
I worked in a Takamine dealership for a while (pre fender takeover), and I did like the way they felt under my right palm. As a caveat though, and again, it may just be coincidence, I had more guitars in for lifted bridges with the pinless design than I did pinned.
Hope that's a help, and didn't come across wrong!