I was entirely self-employed for two years. It's a TON of work. A ton.
First there's figuring out the actual goods and/or service(s) you provide, and deciding what to charge. Then you have to keep taxes in mind. For most legit home-based businesses, you should have a tax number (in Canada, at least) and a registered business number. Those cost money.
Then you have to promote yourself like CRAZY. Get out on all social media, pay for adspace here and there, get out in the local community and promote, whatever works best for your chosen work. Promotion took up at least a quarter of my working hours every week.
Building up a starter budget for supplies, promotional materials and other startup costs is tricky, too. Keep receipts for everything. Taxes.
Oh god, taxes. Ugh. I always owed money, always. Even with claiming everything I could. Taxes were the bane of my existence, and because I sucked at them I nearly got audited last year. Instead they just assessed me, twice, and I wound up owing double. >__<
It's a lot of work. And depending on your biz, it can be really difficult to get the momentum going to make the money you need. Now that AlliePets has become a side job, I'm finally getting the level of business I wanted two years ago, because I've been working hard, advertising and promoting like crazy, and getting portraits done. (Having a pet-related day job has helped immensely too, my boss lets me cross-promote a lot).
There are pros, of course, but they're pretty obvious: Working in my pyjamas. Finnegan at my feet. Having my kitchen within a staircase reach. Lunchtime naps. Setting my own hours and my own to-do lists.
Cons: Budgeting. Taxes. Willpower. Balance. Professionalism.
I found my day job now because I really, really needed the security of a paycheck twice a month. Plus my hours allow me to continue to be self-employed on the side, and between the two I'm more financially comfortable than I've been in years.
My 2c.