Jes, larĝa = wide; granda = large, big; grandioza = grand, great, awesome, wonderful.
But is this a shade of meaning that has emerged since Zamenhof's day? His vocabulary says that "larĝ" is "large, broad" and that "grand" is "great".
I think the nuance of meaning is in English, not in Esperanto.
In English, great has many meanings. It can mean 'awesome' or 'large' or indicate a generation removed. So yes, 'granda' can mean 'great' in the sense of being large.
For 'larĝa', 'broad' explicitly means wide. I don't know if 'large' has any more meanings, but given that it is paired with 'broad', context implies it means 'large width'.