I have recently returned to trail riding with a new hardtail bike having riden a full suspension bike up until 20 years ago. I am back in learning mode and watching some of the excellent mountain bike "how-to" videos on Youtube. With your drop off and crash the problem was one of poor technique and not the bike. In very general terms a full suspension will provide more control than a hardtail but there are vast differences between different models and brands with different amounts of travel in the suspensions provided. The full suspension bike makes it easier to have control on downhill trail sections and brake to keep you speed down. With the hardtail you need to look ahead and pick your line more carefully ahead of time.
Hardtail is less expensive and lighter but less forgiving of rider error.