Also, pars can't be cut quite as cleanly with barndoors or flags as fresnels, especially barndoors. Part of what a fresnel lens does is it refracts the light rays coming from behind it so they emerge much more parallel to each other than they were before going through the lens. Hark:
Because the light rays coming out of the fresnel are largely parallel, you can make a much harder shadow edge than you can with a par. With a Fresnel, it's a bit like the light is coming from a single point source, which is as hard a shadow as you can get, whereas with a PAR spreader lens, it's more like you have a multitude of tiny sources clustered together. Par lenses are made of a bunch of little lenslets, each of which acts like its own little source . You can push in the side barn door quite a lot, but the light from the lenslets on the far side of the lens will still sneak past the barndoor, since each lenslet is emitting light rays over an arc. What you get is a sort of multi-shadow effect at the edge of the cut, where the flag or door is cutting the light from some, but not all of the lenslets.
Of course, if you set the flag a good distance from the PAR, you can get a pretty hard cut, and if you shoot the PAR through a diffusion frame, then the frame becomes the source and that determines the cuttability and shadow edge that you're working with.
The drop-in fresnel lenses that are in some PAR lens sets do not give you the same effect as a real purpose-built fresnel. They approximate it, but they really aren't the same. Those lenses are a bit harder than the other lenses, but not really hard like an actual fresnel.
PARS are distinctly more powerful for your wattage. They're most people's go-to for HMIs. HMIs are so often used with a softbox or a frame that it doesn't matter how hard the beam is, and for daylight situations you often need all the output you can get. When I have a good-sized truck (so rarely these days) I generally get all PARs for my HMIs with one or two fresnels if there's a situation that calls for the simulation of direct hard sunlight. FWIW, the older 12k and 18k HMI fresnels are cheaper to rent than the powerful 12k/18k pars and Arrimax-style lights.