I personally don't think it will matter much which one you pick, I think the key will be to customize yours so that it doesn't look and feel like everyone else's. I would highly suggest you either do it yourself or pay someone else to ensure that your site is completely customized regardless of which one you pick. I see so many people just pick one of these companies and then do nothing to the site other than changing the logo. Your website should be a constant evolution and both of these companies make it easy to change things and keep up with the market/trends.
I had my own site that I created but recently switched over to IC for all the other extra benefits that I didn't have with my Godaddy site. I can't tell you why I picked IC over LP other than just the way I liked the look and feel of the site and also the mobile experience. I also have sites for my buyers and also buy/sell land so the face I could manage multiple sites with ease was also a big plus. Lots of extra marketing options and support is also a plus.........once again I believe customization is the key regardless of which one you pick. Best of luck