Chicke - What you are talking about is what we call the "while we're still friends" conversation - and a big part of it is what's going to happen when things don't go according to plan - because they won't.
You are absolutely correct that the agreement (how partners and others work together and treat each other) is MUCH more important than the agreement (the piece of paper you sign).
The implementations of the Slicing Pie model that I have seen base equity on contribution of money or time (effort). That can lead to some perceived inequities. For example (based on a true story - VASTLY oversimplified) I write some code that code that doesn't work - it takes me 4 weeks. You rewrite the code (using none of my work as a base) so that it works and it takes you a week. I own 80% of the business and you own 20%.
Most readers will look at that example and say "but that's ridiculous". I work with founders all the time ... and this is the stuff that derails companies and friendships.