My hurt back says. ..
If you look at the machine versus free weight studies you'll see that working out on a machine makes you strong on the machine but not the free weight counterpart. Working out on freeweights will make you strong on the free weight exercise and in many cases on the machine counterpart.
However, most exercise physiologists would group leg press and squats together in the same category because they are both linear constant resistance compound exercises. Exercise physilogists would say that the more important difference would be in whether the resistance is variable (ie. uses a cam and cable) or isolated (e.g. leg extension versus leg press).
When you look at the few studies on constant resistance machines versus freeweights like leg press vs. squat you see that the net result is not significantly different.
However, empirical evidence says otherwise. Most strength coaches use squats over leg press in the belief that it is more functional. This has not been proven to be the case when it comes to running. Maybe it is in the case of vertical jump from static position because of the similarity.
The other argument is that freeweight squats are superior because of the neuron stimulation from balancing which incorporates more muscle fibers. This true. However, the balancing also reduces the intensity (amount of weight) whereas in a balanced exercise, like legpress you can use more weight which will make up difference.
The fact is that tension on a muscle is tension no matter whether it is a bar on your back or pushing a platform. The muscle built from a leg press can be trained to do everything the muscle built from a squat can do.
If you add 2 inches to your legs from a leg press, your legs are stronger!
Even if squats are superior for size and strength. How much so? 1% 5%?
I don't know. I make this argument because I squated for 20 years and then severly injured my back. If I could take back every set of squats I did over 20 years I would.
Thankfully, my back has made a full recovery without surgery by some tiny chance about the same as a snowball's chance in hell. I'm here to tell you that the snowball wins sometimes. Not often though.
Along my journey to recovery I've met a lot people who were like me. They grew up in the gym and swore by squats. I did. However, i started getting irritating back pain, muscle pulls, etc... It starts minor. Everybody I met had the same experience. then, bam, you're injured maybe for life.
It seems that some can squat 1,000 pounds and have no injuries. However, if you show signs of susceptibility to back injury from squats, DONT DO THEM.
You can build monster legs on leg presses. Many, if not most, pro bodybuilders don't do squats anymore.
So, my advice is to weigh the cost against the benefit. I personally think leg press is as effective or "close enough" to squats even if injury is not a concern. But, if I'm dead wrong you still have to weigh the risk of injury to your back from squats agains the extra growth you think you'll get from loading your back with hundreds of pounds and squating up and down.