I think Batignolles could be used in any ocassion, from dinner with heels to sport shoes... the neverfull is comfortable but it's less formal.... i personally like the batignolles vertical more than the horizontal, i think it makes u look taller... good luck with ur desicion
I like them both, but only have the BH..the thin straps are mentioned..maybe not such a big deal..the Neverfull might be more a "chuck everything in and go"-bag, whereas the BH can look quite dressy...to be honest, I'd like a Neverful as well...(yep, that was a lot of help, sorry...)
I root for the BH although I'd personally go for the Vertical. Simply because for me, it's deeper and because it's an 'open-bag' meaning without zips, it's safer since your stuff won't easily fall out. I'm paranoid like that hence why neverfull is not for me.