It's difficult to say for a certain which of them will fetch you more than money. If you are an author just starting out, it is going to be real difficult going through traditional publishing route. That's unless you have money to spend already. Otherwise, many agents will throw out your work without even a glance. You can't imagine the number of submissions many of these agents get every month. They barely gave time to go through the works that are submitted to them. If you want to go that path for a certain, then you have to learn the virtue of patience. Many great authors today got rejected countless number of times actually that even includes John Grisham(yeah, you read right).

The statistics of those who get rejected as compared to those who are fortunate enough to have their work accepted might make you give up the thought of traditional publishing entirely. However, with a bit of luck (call it grace, favor), you could get accepted after just few submissions.

The other way, like you've mentioned, is to self publish. This is the way many people like to go through nowadays because it's easier and leaves you in control of a majority of the process. It's even better if you already have an audience for your work. Amazon today has made self-publishing really easy and profitable for authors. You don't have to go through all the down moments and depression that comes with rejection. Your work gets advertised for you and so long as people like your work, you get paid. What's even better, even with a contract with a traditional publisher, there's no guarantee that you'd hit the ground with your work. You may only get the first advance because you book may not gain acceptance. This could be due to your poor writing or poorly marketing campaign on the part of the publishers.

I'd strongly advlse the self publishing route.

I wish you all the best.