To make sure we are on the same page; when you use the term bulldog, I think of the split "shell" type coupler that is basically two hinged pieces that are held in place (while towing) by a large collar that slides back and forth to lock or unlock the coupler.
If you use the lever release (that rises straight up) you will be using an entirely different type coupler that depends on several parts that are located behind the ball and when engaged trap the hitch ball and secure the coupler in place.
opinion: the bulldog coupler is the most reliable and provides the most strength. It is used very often with livestock and horse trailers.
If not kept well greased it becomes difficult to slide the collar to lock and unlock. The thumb lever you mentioned helps provide a mech. advantage but it is just a part waiting to rust and provide problems with movement.
The typical lever that lift ups to unlock and down to lock has parts. They don't fail very often but do have a tension nut that many folks don't know exists until they get down on the ground and look under the coupler.
Typically it has a lower rating in towing capacity than the bulldog style.
recommendation: if you are replacing and can choose; go with the bulldog style. With or without the thumb lever? If you promise to keep it oiled and prefer to push the lever than pull on the collar (usually takes both hands wrapped around the collar and a few grunts) then use the model with the lever for the mech. advantage.
Hope this helps,
Travelers by aluminum roadships, loyalists to one species,
masters of convenience, herdsmen steeped in maintenance and restoration.