Here is a comparison of Greeks to South Italians in GedMatch Harappa World. There is quite a difference between Greek Islanders and Mainlanders. (Surprisingly they don't like mixing

. Anyway the closest to South Italians are Mixed Greeks, which is shown as Greek mean. South Italians and Sicilians are almost identical so I didn't bother to differentiate.
[TABLE="width: 941"]
[TR]
[TD="class: xl245, width: 110"]HarappaWorld GedMatch[/TD]
[TD="class: xl245, width: 79"]Number of Samples[/TD]
[TD="class: xl246, width: 47"]S-Indian[/TD]
[TD="class: xl246, width: 47"]Baloch[/TD]
[TD="class: xl246, width: 47"]Caucasian[/TD]
[TD="class: xl246, width: 47"]NE-Euro[/TD]
[TD="class: xl246, width: 47"]SE-Asian[/TD]
[TD="class: xl246, width: 47"]Siberian[/TD]
[TD="class: xl246, width: 47"]NE-Asian[/TD]
[TD="class: xl246, width: 47"]Papuan[/TD]
[TD="class: xl246, width: 47"]American[/TD]
[TD="class: xl246, width: 47"]Beringian[/TD]
[TD="class: xl247, width: 47"]Mediterranean[/TD]
[TD="class: xl246, width: 47"]SW-Asian[/TD]
[TD="class: xl246, width: 47"]San[/TD]
[TD="class: xl246, width: 47"]E-African[/TD]
[TD="class: xl246, width: 47"]Pygmy[/TD]
[TD="class: xl246, width: 47"]W-African[/TD]
[/TR]
[TR]
[TD="class: xl186"]Greek, mainland[/TD]
[TD="class: xl248"]3[/TD]
[TD="class: xl249, align: right"] -[/TD]
[TD="class: xl249, align: right"] 6[/TD]
[TD="class: xl249, align: right"] 32[/TD]
[TD="class: xl249, align: right"] 25[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl249, align: right"] 26[/TD]
[TD="class: xl249, align: right"] 11[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[/TR]
[TR]
[TD="class: xl186"]Greek, Islands[/TD]
[TD="class: xl248"]5[/TD]
[TD="class: xl249, align: right"] -[/TD]
[TD="class: xl249, align: right"] 9[/TD]
[TD="class: xl249, align: right"] 38[/TD]
[TD="class: xl249, align: right"] 14[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"] 1[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl249, align: right"] 23[/TD]
[TD="class: xl249, align: right"] 14[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[/TR]
[TR]
[TD="class: xl186"][/TD]
[TD="class: xl248"][/TD]
[TD="class: xl249"][/TD]
[TD="class: xl249"][/TD]
[TD="class: xl249"][/TD]
[TD="class: xl249"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl249"][/TD]
[TD="class: xl249"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[TD="class: xl251"][/TD]
[/TR]
[TR]
[TD="class: xl186"]Greeek, Mean[/TD]
[TD="class: xl248"]8[/TD]
[TD="class: xl249, align: right"] -[/TD]
[TD="class: xl249, align: right"] 8[/TD]
[TD="class: xl249, align: right"] 35[/TD]
[TD="class: xl249, align: right"] 19[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl249, align: right"] 25[/TD]
[TD="class: xl249, align: right"] 12[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[/TR]
[TR]
[TD="class: xl186"]Italy, South[/TD]
[TD="class: xl248"]5[/TD]
[TD="class: xl252"]-[/TD]
[TD="class: xl249, align: right"] 8[/TD]
[TD="class: xl249, align: right"] 32[/TD]
[TD="class: xl249, align: right"] 17[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl249, align: right"] 27[/TD]
[TD="class: xl249, align: right"] 13[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl186, align: right"] 1[/TD]
[TD="class: xl251"]-[/TD]
[TD="class: xl251"]-[/TD]
[/TR]
[/TABLE]
We can see that there is not a huge difference between Greek Mean and South Italian. Greeks have definitely more Anatolian Bronze/Iran Ch/CHG with higher Caucasian and Lower Med. Which is logical being closer to the source. This makes S Italians being more EEF. Also we can see Slavic migration/WHG/Steppe influence in higher NE Euro in Greece, especially Mainland Greece.