I kind of think differently. Both LV shoes and CL shoes like to be known for their brand. LV has lots of blinged metal-ware, monogram, or some form of LV sign on the shoe. CL just has it on the sole.
Width - LVs are normal to wide
Heel height - LVs are clearly incomparable to CL's 160 height now. If you go higher than 3 inches in LV shoes, they also tend to be uncomfortable.
Style - LVs are typically pretty casual to conservative. CLs... are pretty wild these days. Most CL's shoe design have a sexier silhouette due to its high pitch. I don't think LV's are nearly as sexy looking as CLs and I think few would disagree...
Comfort - LVs are in general almost all more comfortable than CLs (toebox), except for LV's sandals which are often horribly made. LV's monogram or vachetta leather on shoes are just the worst idea ever.