hi chico,
   i have been listening to this song since i was a small child(1953)and my favourite version is gigli's. enrico caruso did it before him and i must confess, i don' t know of gino becchi. you have the words right except for a few:

                     vorrei baciar i tuoi capelli neri
                     le labbra tue e gli occhi tuoi severi
                     vorrei morir con te angel di dio
                     o bella innamorata, tesor mio.
                     Qui sotto il vidi ieri a passeggiare
                     e lo sentivo al solito cantar:

and at the very end the words are:
                     
                     stringimi, o cara, stringimi al tuo
                     cuore, fammi ecc.

and you are right, it is one of the most beautiful/haunting songs ever written. that' s what i told luciano pavarotti in person in 1978 at a time when he was sing only operatic pieces.