From what I can recall of previous debates, neutral Italy (say Benito decides not to do anything in the first couple of years whilst he rearms/upgrades the Italian army, and then he manages to restrain himself and sit on the fence for a while whilst he watches how the fighting's going) means a lot less hassle for British shipping in the Mediterranean, and Britain possibly only needing to mop up any German holdings in Africa. (I'm not sure what would happen with regard to the Vichy French.
)
With the Italian fleet not committed to the Axis, the British may be able to afford not to be in such a rush to sink the French at Mers-el-Kébir, resulting in possibly better relations with the French (Free or otherwise).
Meanwhile, Adolf gets to avoid the distractions of North Africa and Greece (plus Crete in the latter case, which was a bit rough on the German paratroops) and has another neutral country abutting the Reich with which he can trade for raw materials that he can't get from countries his armies are currently occupying.
The Italians get to be bribed by and to sell things to both the Reich and the British, making money without losing any troops. (Well, not losing any troops, always assuming that since his African empire isn't under attack, Benito doesn't feel pressured into starting something in Albania.)
I think I've seen suggestions somewhere that Italy was months away from discovering Libyan oil in the OTL, but that the geological mission that would have found it was cancelled when Benito threw-in, militarily, with Nazi Germany.