For women: I find that Loro Piana has more color options. BC sticks to a few color ways that is apparent when you go in one of their stores. BC also likes to use pailletés that go great with their monili. In my opinion, BC pieces are very Italian with a very beautiful and unique balance of sparkle and rustic. In my mind, the iconic BC look is a sparkly silk skirt with a paillette jumper or leather biker jacket. Loro Piana is more simple and elegant with a greater emphasis on the material and color. Material and feel wise, I find BC is often a bit thinner than Loro Piana. Loro Piana also offers many types of cashmeres while BC sticks to one. Baby cashmere from Loro Piana feels amazing.
For men: once again the color options at Loro Piana are more extensive than BC. For men (like women), there are the thicker knits and super thin knits, but not too many in the middle at BC. I have found that BC pills less than Loro Piana.
Overall, between the two, I think it really depends on the style you want for your jumper. For a basic, I would go for Loro Piana as there is more selection of both types of cashmeres and color.
On a tangent, but I was pleasantly surprised by Hermes cashmere jumpers for men. Compared to both Loro Piana and BC, the cashmere was the finest at the touch.