I own the Muse in Black Buffalo and the Mulberry in Oak Brown. I LOVE them both. I do not see the Bayswater being carried around everywhere I turn here in L.A. but the Muse is EVERYWHERE, unfortunately, and sometimes the people carrying it are not exactly "designer handbag" looking people, which makes me wonder.....fake?
I love the Mulberry Bayswater- mine is the oversized version, bought on their online site. It is a classic, and I receive many compliments when carrying the bag. I do not think of it as a "casual" bag, especially if you buy it in black.
As much as I love my Muse, I would purchase the larger size Bayswater. It is the ultimate "Tote" in shape and the leather is beautiful. I am just seeing way too many Muse bags and it's really bugging me. I might give mine a "vacation" for a season or two.
Tough decision- they are both iconic bags. Good Luck!