Feel free to use both the squat and leg press in the same workout. In fact, Art Jones (among others) suggest that leg extensions, leg presses and squats, be done it that order. One right after another in tri set style. Excellent muscle builder. I and some Bud's have used it in the past with good results. Might want to take a little caution when first trying this type of training, very demanding on the body (CNS). Throw in standing leg curls and manuel lying leg curls for the ham's after the tri set's are done.
Depending on what type of leg press device your using, the main focus will be on the quads and the hips to a lesser degree. The back is braced quite well. Squats put greater demand on balance and a excess of supporting muscles, more than the leg press would ever do. Simply because the weight load is resting on the top part of the body (neck/traps/shoulders) making it more of a gravity resistence and balance exercise. And there is no brace or support for the back. Squats take much more energy than the leg press. When done right, the squat can add muscular weight to the entire body as well as increasing the cardio abilities to a higher level. Really no need to go arse to ankles when squating, no extra benefits.
Everyone is build different and leg bone length, muscle inserts, etc will have a bearing on how squating will affect the muscle involved. So does squating styles, high on neck/traps...low on the middle traps, etc. Shorter men seem to have a better body design advantage when squating. Some guy's will feel squats in the quads but not the glutes and some the other way around, etc, etc, etc.. If squating with the heels raised on a 2" block, for example, more of the focus will be on the quads themselves. Front squats are another example where the quads take the blunt of the work. Good Luck.