To start with, you also need to break out conventional loans into conforming and non-conforming.
Lets start with non-conforming. There are no limits to these. Borrowers and lenders agree to any terms that they want. The lenders can apply any underwriting standards that they want. Thus, these are the most flexible, but also more expensive because of the advantages of the other two categories.
Conforming conventional loans are not guaranteed by the governement, but they can be sold in the secondary mortgage market at the drop of a hat. Because of this liquidity, lenders are willing to accept lower returns. However, they also have less flexibility. THey have to meet the underwriting standards established by the GSEs fannie mae and freddie mac. THese include loan size, loan to value ratio, income and debt ratios, credit scores, and property type restrictions.
FHA mortgages are more expensive and they are guaranteed by the federal governement. Some underwriting requirement, such as income and debt ratios, are more flexible, others sich as loan size and down payment, are more restrictive. These can also be easily traded in the secondary market.
So, in the end, you are trading off flexibility for cost.
I teach real estate finance at the university level