Drop biscuits have a very nubbly crust that develops an interesting texture and chew when baked. As a rule they are also chewier than properly made patted or rolled biscuits. Drop biscuits are ideal for a brush with something nice before baking -- say honey mixed with melted butter.
In my opinion the idea that patted/rolled biscuits should be handled as little as possible is something of a myth. They are very short, but not so dry as to be as fragile as something like a pie crust.
It's true they should not be overmixed, nor overhandled, but they benefit from a few gentle kneads -- and if you want a flaky interior, you'll have to give the dough a few turns.
You do want to get them on the sheet and in the oven without much delay if you're using baking soda or single acting baking powder for any part of your leavening as it starts losing loft potential just sitting around.
At any rate, the rolled or patter version demand a lot of "touch" and a certain amount of timing to get them right.
Drop biscuits are, on the whole, more forgiving. I haven't made them in ages. Maybe this week.
BDL