How does a running shoe work out for you while heavy squats or leg press? Since they are made to absorb shock it will also absorb power you generate. I've read the hard soles are best for lifting. Even flat w/o cushion ones are better.
Here's an article :-
Wrong Shoes: Running Shoes. The air & gel filling is great for reducing impact shock from running. But bad for lifting. Running shoes will limit your strength & prevent good lifting technique.
Unstable. Soles are squishy so you can't predict their behavior on each rep. This makes it harder to control your technique and lift properly.
Power Loss. The soles absorb the force generated against the floor instead of directing it towards moving the weight. You lose strength.
Dangerous. Higher risk of injury, especially with heavier weights, since the soles make it hard to balance yourself and are less stable.
Benefits of Good Lifting Shoes. Good lifting shoes have incompressible soles. They must be non slippery, have excellent support and fit snug. Benefits:
More Stability. Better traction against the floor and improved balance under the bar because the soles are hard.
More Strength. Your heels will sense the pressure of the weight better, which will make your legs contract harder.
Better Technique. Good lifting shoes will fix many technique issues. You'll sit back better, your heels will stop coming off the floor, ...
More Safety. Better balance, better technique, ... All of it decreases the risks of injury during lifting.
Best Shoes for Squats. Depends on how you Squat. But the sole should always be incompressible for maximal stability, power transfer & technique.
Low Bar Squats. More leaning forward, less depth. Chuck Taylor's are the best shoes for Low Bar Squats. Recommended by Louie Simmons.
Olympic & Front Squats. Torso is more upright, more depth. Shoes with heels make it easier to go deep. Examples: Adidas Adistar, Do-Win, ...
Best Shoes for Deadlifts. The closer your feet to the floor, the less distance the bar has to travel and thus the more weight you can Deadlift. That's why thinner soles are better. These should be flat & incompressible.
Barefoot. Can't get closer to the floor than this. However barefoot is not allowed on competitions. You'll usually have to wear socks or slippers.
Ballet Slippers. Less slippery than socks because ballet slippers usually have a rubber sole. But still very thin.
Chuck Taylor's. Soles are flat enough to work for Deadlifts. However the bar will have to travel more distance compared to slippers.
Chuck Taylor's. These are the best all around shoe. Chuck Taylor's are efficient & cheap. And they will last forever as lifting shoes.
Hard Sole. Sole is thin, flat & incompressible. Your feet are close to the floor. You'll feel your feet better during lifts: more stability & control.
Strong Canvas. This allows you to push your feet to the outside on Squats which helps keeping your knees out and activating your glutes.
Ankle Mobility. Full ankle mobility with low tops Chuck Taylor's. If you buy high tops, leave the top part unlaced.
Do You Need Shoes With Heels? Olympic weight lifters wear shoes with heels because these make it easier to hit depth on Olympic lifts like Power Cleans, Olympic Squats, Front Squats, Overhead Squats, ...
However for low bar Squats and Deadlifts, shoes with flat soles are better. If you're serious about Olympic lifting, consider weight lifting shoes like Adidas Adistar or Do-Win. They'll make things easier.
Barefoot Lifting. Lifting barefoot strengthens the small muscles of your feet & improves ankle mobility. I always lift barefoot except for Squats and unless it's too cold in my gym. I also walk barefoot all the time at home.
Try lifting barefoot at least once. You'll understand the importance of good lifting shoes. Is it safe? If a big plate falls on your foot, it will hurt whether you wear a shoe or not. Be careful and it won't happen.