In most cases, I like using an existing system. But the system I'm currently working on is a result of frustrations in PbEM and non-asynchronous games. Either you slow things down, or everything becomes purely narrative. I'm trying to find a middle ground.
The reason that normally I go with something that's already there is because of my play style- I only mine things in other systems for ideas, as knowing a system, you can really get an idea about it's strengths and weaknesses over time with it. A new system you have to start all of that from scratch.