Assuming the U.S. (since that's what your profile says), the differences are:
- If you own a corporation, there's more reporting to the IRS and state (quarterly for small business and regular corporations) and you pay payroll taxes quarterly (or more, depending on your payroll amount).
- Corporations and LLC's can take more exemptions than 1099's (technically, a corp-to-corp arrangement also often receives a 1099 so it's more accurate to call "1099" self-employed or schedule-C [schedule-C is where one reports earned income for which they did not receive a W2]).
- Generally, you get paid a lot less as a W2 contractor. There are various reasons for this (vacation, healthcare coverage, etc.)
- Besides the quarterly (or more) payroll tax deposits to the IRS and state, you must also prepare the year-end W2 and W3 for the employees (yourself) and the social security administration. And, of course, you must do the year-end tax return for the fed (1120) and the state (these are due March 15 instead of April 15 -- a month earlier).
- You (usually) must invoice your client (if you're working through a contractor, then you'd be invoicing them, not the client you work at), for each period specified in your contract paperwork. Often it's every two weeks, but could be less or more. This is over-and-above the timesheet requirement.
- Corp-to-corps are usually paid net-30, meaning you won't see any money until 30 days after your first invoice is sent (assuming they pay on-time). So, if the contract says you invoice every two weeks, and the payment terms are net-30, you won't see a dollar until approximately 40-45 days after you start working. This can be a killer if you're not prepared.
The risk and cost to you as a W2 contractor are nill. Usually, to do corp-to-corp, you must carry your own liability insurance (for me, in AZ, it's about $1,500/yr, yours may vary significantly depending on the nature of the contract work and your state). There are more risks and more paperwork as you move from W2, to self-employed/schedule-C/1099, to corp-to-corp, as well as more advantages. There are a bunch of start-up costs for a corporation, depending on which state you do it in (CA is very expensive, whereas AZ is pretty cheap). In some states it's easy enough to do on your own, in others, it's easier to have a lawyer take care of it for you.
Doing payroll can also be a pain as a corporation. You can do it by hand (I did for an entire year), or you can get QuickBooks and let it do it for you (that's what I do now, and it's way easier). Also, you'll probably need an accountant, although, again, I did my own accounting for a while (it's easier if you're by yourself. As soon as you have a partner, it becomes complicated. More employees are actually not at all difficult, just partners/joint owners because of the Schedule K-1).
As a corporation, it's also a good idea to have a separate bank account and credit accounts for the corporation to make sure your stuff stays separate. The IRS doesn't like it when funds mingle and with separate accounts it's easy to show they haven't.
As you can see, it's not merely just, "uuuum, I choose option B,", there's a lot more to it.
One last note: if you do just plain 1099/self-employed, you will probably need to make quarterly estimated tax payments or else you'll owe interest and penalties when you do your personal 1040 at the end of the tax year.
Edit: one last thing I thought of re-reading one of the other answers: as a corporation, it's your responsibility to make sure your clients pay you. Sometimes (a lot of times) they pay late. Sometimes they don't pay at all. It's not unusual to have clients go 90 days past due on invoices. You need to build up a cash cushion so you can handle that. You also have to weigh your ability to deal with deadbeat clients. This is probably the worst part of doing corp-to-corp contract work.