Pros: As a self-published author you have control over every decision in the book making, publishing and promoting process.
However every pro has a con; with the extra control comes greater responsibility. With every decision there is a lot of leg work, that as a self-published author you either have to do yourself or pay someone else to do. So there is either a financial cost or a time cost.
Another pro: You can plan your own timetable; with complete control over release dates and promotions.
However: it can be easy to get off track when no one is kicking you up the arse to get your book out there on time. It's not easy getting your name, your book and your general brand known so having help to do that can be really beneficial. Especially when you are starting out.
Another Con: There are certain parts of the publishing process that are best done professionally - for example your cover - you want it to look eye catching and professional.
However: as a self-published author you can pick and choose what jobs you do yourself and what jobs you pay someone else to do.
I'm quite comfortable with the idea of self-publishing. With it there are challenges but there are definitely rewards too. When self publishing you have to have self control. There's no one else there holding the reigns for you. But I'd definitely recommend it for any new authors out there.