‘Best’ is a loaded and not a very meaningful term. Both are well-made and have good fit & finish. Thermally, they are almost indistinguishable. In no particular order, here’re what I vew to be the salient differences.
Interiors Yes, LC usually has white enamel linings, and Staub black. I “get” the theoretical advantage of white–being able to see fond better. But I’m with eugene on this–there aren’t many things that would make white a clearly better choice, at least if you have decent kitchen lighting. OTOH, black would be advantageous for hiding scratches, stains and scuffs. FWIW, at one point, LC claimed its black enamel was more durable and held seasoning better than its white.
Covers I like the Staub covers and knobs a little better. Again, pretty minor, IMO.
Colors I find the Staub colors richer and deeper, and they don’t change them on a whim, so you stand a better chance of finding same-colored pieces. But the LC palette appeals to many people as a clear preference.
Selection When I was into LC, I assessed that LC offered a wider selection of shapes and sizes. I suspect this is still the case. So, if you want brand and/or exterior colors to match, and you must have some more specialized piece, LC may be a better choice.