Well, it's a tenor, the vibrato is less than Bechet's, and there's not nearly as much "filigree", but to my ears, you could make it into Bechet w/o a whole lot of effort, just as you can make Little Walter into Hodges int Bechet.
Bechet is highly underrated as an influence on everything, I think.
I agree about the importance/value of Bechet - for years I have felt Armstrong gets credit due Sidney. No argument about his influence. I just think Prince is worthy.