Olympic lifting shoes, which are weightlifting shoes, can indeed make a difference. However, this difference will only be beneficial if you are suited to using weightlifting shoes (in regards to your foot anatomy), and if you are using them correctly with the proper body form.
The main advantage and difference that Olympic lifting shoes provide, is a deeper squatting position that enhances good lifting form. This way, your chest can remain higher up, with more ease, helping you lift the weight properly.