I would say the answer to this good question is quite complicated.
For the lower price-points, on single family residences in respective communities, I can say with total confidence that banks will flat out not accept FHA offers, and even 20% down offers have relentless competition. I'm seeing most sellers hold out for the highest price they can get, often above fair market value, and then deal with it later if it doesn't appraise.
For this reason, among others, banks and other sellers seek all (or mostly) cash buyers as their first choice, because lender approval will not be a deal-breaker. They have been able to do this with relative ease, because they're getting 10+ offers within days putting a sign up.
The lower-end markets have been greatly impacted by government and banking actions that have created an artificial short supply. With such a short supply, and such a great demand, investors and mostly cash buyers are sweeping up the good deals. The rest of the first-time home buyers are considering themselves grateful for opportunities to scrape up what's left over.
For mid range homes, you can get fair market value with 20% down, but still need a healthy down payment fi you want to compete.
For high-end homes, you can't qualify with less than 20% down, and more in most cases... but here, the buyer is king as the top end of the market is flooded with supply.