I have to say that am I hosted on a shared host that uses CPanel.

This sounds very much like you will not have access to a persistent back-end. In that case you should be aware that running Plack-based applications without a persistent back-end incurs a significant performance penalty. See this old but still relevant discussion which also lists some lighter alternatives.

If somehow you can run a persistent back-end then yes, that's going to be faster. In that scenario, using a PSGI-based solution (plack or otherwise) effectively de-couples your code from any one specific front-end so it would be the way to go.