It seems easier to book on Loco2 as compared to Renfe. Is there any price difference or other notable difference depending on where you book?
You didn't ask about the best way to make this journey, if you had I would have recommended the bus over the train (4h30/5 hrs, €19.95/€44.85: https://www.alsa.com/en/web/bus/coach/madrid-granada).
As for booking trains through the RENFE or Loco2 website, whichever you use, you would be travelling from Madrid to Granada by RENFE (the train OPERATOR)! You asked whether there was any price difference between these two and the answer is "no". I don't see what other differences there could be given that Loco2 doesn't run trains - obviously your booking would be for a RENFE train!
That said, personally I always prefer to book directly with the operator concerned, so if taking the train, RENFE: but if you can't manage RENFE's website, then Loco2 is the best of the available booking agents.