It's like this, please don't make noise.. per favore is a phrase
I beg you(literal) is a verb or Could you please stop making noise? si prega di fare silenzio.
In practice both are the same but si prega di is impersonal it can't be like this:
if you tell your friend, you don't say si prega di mangiare, you say eat please.
if it's an order for anyone, you can use both, si prega di non mangiare. non mangiare per favore
hope it helps, ciao