Hi. I use both of these exercises with most of my clients. Like ANY exercise, if done incorrectly each of these could cause problems/injury. The keys to my mind are teaching proper technique, AND not overloading the exercise.
I do both as well.
With deadlifts, I have my own philosophy as I try to teach them to all my clients even if the ‘weight’ is often little more than a broomstick. My thought is that there are situations when people need to be able to lift things over a barrier where the command of ‘lifting with your legs’ simply does not work. Getting something out of the trunk of a car or lifting a baby out of a crib are examples. I use it to teach maintaining a neutral spine and engaging the core while being forward flexed and unsupported.
Squats are definitely part of my clients’ workouts as well as my own. They are very functional. I use deadlifts only occasionally, and only with those clients who have spot-on perfect form. Although it looks like a simple exercise, proper form can be difficult to cue–and I can think of other exercises that work just as well.