I like anything I can operate one-handed, meaning I never buy back lock knives.
I was buying liner lock knives before other one-hand lock types and I have no problem with them. I don't have a problem with frame locks either from a lock standpoint but it bothers me that one side of the knife can have a nice scale while the other side doesn't. I've had PM2's for awhile and I like the knife but I didn't rate the lock as anything special until more recently. Now I have a few Manix 2's with the BBL and I've come to appreciate them.
Knives with liner lock, frame lock or compression lock seem to operate similarly- the lock has a ball detent that rubs against the side of the blade and adds friction. The blades all feel the same when opening them, not much way to change that feel. The BBL is somewhat unique in that you can change the detent and the way that feels by reshaping the blade tang. The lock also starts to engage before the blade is completely open, with liner lock the lock can't operate until the blade is completely open and if you open it slowly it will not engage the same. When closing the knife I hold it with the edge pointing down, operate the lock, the blade swings part way closed, I finish closing it with my thumb- very quick and easy and foolproof, unlike a liner lock. I owned a Para2 for over a year and it wasn't until i was using the Manix2 that I discovered that the easiest way for me to close the Para2 was basically the same way.
I voted BBL because it is somewhat unique but I like all locks other than back lock and lock type is not a consideration when I am buying a knife.