I don't have a number to say as a percentage, but it definitely have some impact. Not the first time I precent it to upper management and Asana won purely based on "looks". ( You see, those in the management don't actually "DO" anything, they look at things and if they dislike it they will disprove it, whether a tools is decent to use is not their problem )

I felt Basecamp are aiming at different market to Asana. Basecamp are for consultants or freelances with many clients. Asana are aiming at SMEs and Enterprise.