Which is better for you? Which one is cheaper? It really depends on you, your credit score, your down payment and sometimes even the property you want to buy.
Both are basically the same 30 yr mortgage, but there are pros and cons to both. FHA has an upfront mortgage insurance premium of 1.75% that is added to the mortgage. Conventional mortgages don't have that. Both have monthly mortgage insurance. However, FHA's monthly mortgage insurance is 1.25% of the mortgage amount. Conventional mortgage insuranced is only required if you have less than 20% down and the rate varies based on loan to value and credit score.
FHA requires a minium down of 3.5% and it can be a gift from a family member. That is one of the biggest benefits to a FHA mortgage. Conventional loans typically require a minimum down of 5%. Under some circumstances you can do 3% down, but you have to meet income and credit score criteria. Conventional loans will not allow a gift unless you have 5% of your own money into the transaction or you have a gift of 20%.
FHA also doesn't give the same adjustments to the rate that conventional loans do. If you have a 660 credit score, the rate usually isn't affected on a FHA mortgage, however on a conventional mortgage, there will be a rate adjustment of about .375% depending on your down payment. That rate will stay the same for 30 years or until you refinance your loan. Mortgage insurance will go away once you pay your mortgage down to 78% for FHA loans and 80% for conventional. If your credit score is lower, it may be cheaper for you to use FHA financing than conventional.
For those that have had a bankruptcy or foreclosure, FHA may be easier. FHA requires 2 yrs after a bankruptcy and 3 years after a foreclosure. Some conventional lenders require 7 years after a foreclosure.