Hi transposen,
All else being equal and if I didn’t have bedbugs already … I would personally choose a protector over a full encasement because it is more breathable but of course this is also a tradeoff between the “risk” tolerance of each person and the differences between each type. If I actually had bedbugs then there is no doubt that I would use an encasement as part of the means to eliminate and protect against them (it will starve the ones that are in the mattress and protect more from entering because a bed bud infestation is usually not limited to the mattress).
It’s main benefit is that it reduces exposure to dust mites (and their “waste products”) and eliminates the ability of any bedbugs in the mattress to feed on you over the course of the night but the tradeoff is less ventilation and breathability because the material needs to have a micron size that is smaller than the dust mites and bedbugs or have no pores at all.
Some of the different types of mattress protectors (including the “membrane” type such as malouf) and the tradeoffs involved with each type are in post #89 here.
Phoenix