And in particular,
I want to continue browsing sessions between making calls ets
So should I perhaps choose one browser over the other.

At the moment I'm using the BB option as it allows me to modify home page to (google) whereas the awfulness that is T mobile's version
constantly suggests pop music/chat
(whatever that is)

but unfortunately it continually closes down whatever I'm gawping at.

I use the BB Browser and Opera Mini depending on what I'm surfing. I hardly ever use the wap site.