I haven't flown anything larger than a Cobra yet, but so far I think docking manually is very quick and quite enjoyable most of the times (at least as long as I don't forget the docking request

). I haven't tried the docking computer yet because I have never felt the need for it.
Just for comparison
In original Elite docking the Cobra was a lot of precision flying: fly by the station at the correct angle until you had the "dot" in the compass showing the station right behind you. Stop and turn around. Correct the approach angle until the station entrance was dead centre, start rotating the ship at same speed as the station and pray you don't overcompensate while you accelerate. As soon as you made even a small mistake near the letterbox: Boom! Here the docking computer really was a very useful tool that worked miracles.
In Elite Dangerous docking a Cobra is quite easy. I still use a similar approach as before, but don't follow it as precisely because it's not necessary. Finding the entrace is easy and correcting the approach is easily done with the lateral and vertical thrusters. The opening to the station is much larger, and even if I'm not careful the worst thing is a little shield damage while I scrape along the entrance as long as I keep the speed reasonable. Nevertheless I especially like going in at higher speeds and trying to set down in one fluid motion. Don't get it right all the time of course

In my opinion the only reason I would use a docking computer would be for instant docking to save me time. But what I've seen from videos docking manually is much faster than by computer. Anyway: IMHO docking manually is one of THE major improvements toward the previous version and it adds a tremedous lot to the atmosphere of the game.
The only thing I really don't get is why most pads on the outpost are oriented in a way so that I always have to fly past, close to or around structures from the station, instead of flying in directly from open space. That's a bit like putting a large apartment building right in front of the runway which the pilot has to fly around in order to land. (Or a bit like the old Hong Kong Kai Tak airport).