I think Tony Bennett was more clasically handsome (and probably taller, lol), but Eddie wasn't bad, he was kind of cute in an ethnic, Italian way, although I know that he was Armenian IRL.
The thing I always hated about Carmine's looks was his hair. Especially in early season four, which I'm watching now, he had this huge, Bozo hair, and it was always kind of flat on top, which magnified the Bozo quality of it. He had thick, curly, coarse hair, the kind that becomes unruly when it isn't maintained, and that is exactly how it looked in these episodes--unruly, which did not add anything to his otherwise pleasant, nice guy looks. Had it been cut much shorter, even with the big '70s sideburns that he sported, he would have looked much hotter, IMHO.
Now, if we want to talk about REALLY unruly hair, let's start a thread about Mr. DeFazio...π±