I almost always start with creating a new system, because I'm interested in tinkering and experimenting. The games I make usually start with a question about different ways to structure the RPG experience. "What if we have two players control one character?" "What if you use the board game Mastermind to model scientific discovery?" "What if we use this mechanic to model this experience?" etc. Then I build from there the mechanics needed to support that idea.
I usually only use an existing system when the initial question/experiment relates to the system's base system. "What if you used Cthulhu Dark to model time travel?" "How much can I remove or change from this game before it stops being recognizable as a hack of the original?" "If I stick this subsystem from game A onto game B, will that make the experience we want?"
The advantage of using an existing system isn't that it's simpler. It's not. You still should be doing the hard work to understand each component and critically examine it and think about the role you want in the game, just the same as you would have to do if you were making your own game from scratch. But it has the advantage of learning about a different designer's thoughts. Taking apart their game and rebuilding it opens you up to ways of doing things you wouldn't think of on your own.