Balenciaga would have to be up there. The leather on my Anthracite Twiggy bag is very soft, lightweight and lovely. Gerard Darel also has lovely leathers, but my 24 Heures is a little bit heavier. Extremely hard-wearing, rain-resistant and beautiful style. The softest bag I have ever owned is actually a Mauve Burberry satchel, which is next to me as I write. But I haven't a pic and don't know the name of the style because it's a sample from a previous Christopher Bailey collection for Burberry.
I would say that is a toss up between my Balenciaga's and my Marc Jacobs Turnlock Teri - with the MJ being the most supple of the two. Love the MJ leather but it's red and I have to be careful for color transfer.