FHA and conventional loans are two different programs with two different target markets.
Conventional- usually for the better qualified borrower. The credit, income, down payment requirements are more strict. It has higher loan amounts and, if your LTV is over 80% MI is cheaper and can be dropped once the loan balance is less than 80% of the property value. If you have little credit or bad credit, exceptions are harder to come by. Sources of down payment are also more lenient- FHA allows more to be from gifts.
FHA-is government insured and, while it was traditionally for first-time home buyers that is not a requirement; however, there are more rules on owner occupation. You can sell your first home and pay off the FHA loan and still do an FHa on your next home (rules do apply though). For people with poor credit or little credit, there is more leniency (credit score minimum is 500 whereas Fannie and Freddie have minimums of 680), they allow you to carry more debt (41% of your monthly income whereas the conventional, especially now are holding to 38%), you can borrow a higher percentage (97% loan to value is the norm whereas conventionals are 80% plus, in conventional loans the mortgage insurance companies can deny you even if the lender approves your loan. FHA has one approval process so if you have an 80% loan to value or a 90%, you don't have to worry about another set of qualification standards to meet.). FHA will permit you to get the entire down payment from gifts whereas fannie and freddie will not. FHA does not do second home or investment loans, they have longer owner occupancy requirements, they have different requirements for the appraisal (there is though a rehab loan program that allows people to buy homes with problems and borrow the purchase price plus the rehab costs), MI on FHA is more expensive and cannot be dropped even if you pay off a large chunk of the principal or the property value increases.
It comes down to FHA is a government insured program whose mission is to help as many people as reasonably possible to have a chance at owning a home. Conventional loans are a business profit making prospect and,they are only going to do loans where the investors will make a profit amd not lose their investment so they want the "safer" loans.