This is a question which I have been asked several times recently. There are advantages and advantages to both, so here is some of the most common answers between the two
Self Employed
*Easy to set up, you need to register with HMRC for self Assessment
*Taxed Profits, @20% and 40% for higher earnings
*You are liable for all debts of the business, which could mean if the worst happens your personal Assets could be at risk
*Can take money out of the business freely for personal spending
*Complete a Self Assessment Tax Return Every Year
*Accounts easier to maintain
Limited Company
*Separate Entity, your personal assets are safe
*Tax rate on Profit 19% (Paid by Company)
*Set up a Limited Company with Companies House, which means your details will be publicly available
*Cannot take money from the business freely, usually paid through PAYE and dividends from the Profits
*Can be easier to get funding
*Complete Annual Accounts to Companies House and a Corporation Tax Return to HMRC every 12 months
*Bookkeeper/Accountant recommended more complex account management
These are the main points which are often asked, if you have any particular questions regarding either I am quite happy to answer them.