I like your second idea. This will vary so drastically from app to app. For some apps you might need the designer to make a logo and a few images (assuming you use out of the box icons). That could be a 95/5 split on effort. A game or super visual app COULD go 50/50 on time expenditure but that's probably rare. Also, depends on the skill levels. Should you assume that value per hour are equal?

For instance, if I were to bring a pro designer onto a project that he was only doing %25 of the time on, I'd probably give him 50% cut (because his time is worth double what mine is). Ultimately, kind of a complicated question.

I don't think time is a good metric as some people are faster than others, but the impact of what they do matters more. Also, a "rockstar" designer or developer is potentially worth more than a novice. At the end of the day, there is no easy way to quantify things (yes, I know -- a non-answer) but things will be a lot easier if you both feel as if you are getting your fair share.