The crafter, unlike the dropper and dispenser, has no 4 gametick output delay. This discounts most "subtick" interactions between droppers and crafters. This may just be intended behavior.

The first attachment demonstrates that crafters can move certain items, such as redstone blocks, with basically no delay. Droppers, on the other hand, always take an extra 4 gameticks. This makes crafters better than droppers at their own job in certain scenarios.

In the second attachment, a redstone block is stored inside the dropper, and the dropper is pointing into the crafter. Most veteran Minecraft players would expect the crafter to spit out its redstone dust immediately after the dropper pointing to it is activated. However, the crafter is actually activated before the dropper, so the redstone block just sits inside of the crafter after the dropper powers. At first glance, this feels unintuitive to me.