In a nutshell, I would describe
Bamboo as a cooler white,
Milk as a warmer white. I think the hardware colors reflect this since it's gunmetal and gold, respectively.
From what I remember in stores,
Bamboo was a 'dirty white'. It has a very faint grayish tint to it due to the distressing, I think.
Bamboo leather is similar to the fall '09 (I think it was) leathers i.e. Bordeaux, Oceano, Timoro, etc. So it has that "crinkled" look going on. Not as extreme as those '09 Magnolias though.

It's semi-matte leather and I know this type breaks in nicely overtime and gets softer with use. I love this type of Treesje leather.
I tried the Mason in
Milk too and was not a fan! There were no issues with the style or color. The color is a warmer off-white or eggshell. I just could not stand the finish on the leather. At first glance,
Milk appears to have a smoother finish, but the leather felt completely coated and REALLY stiff IMO. I quickly passed on these series of leathers.
Just based on leathers, I prefer
Bamboo over
Milk. If you don't mind distressing, I'd recommend it. Plus since it's not pure white, getting it a little dirty might possibly blend in?