Well it's really your thrust to mass ratio.
As for manoeuvrability it'd probably be equal. Every newton of force going in one direction has to be countered in order to stop travelling in that direction. If the Mass to Thrust ratio is the same it really just comes down to how quickly they can turn the vessel to then thrust in the other direction.

Though sci-fi ship battles a-la EVE/Mass Effect/Star Wars/Battlestar etc is really just space submarines. Nobody takes into account orbital mechanics when fighting near a planet/star/other gravitational body. And small fighters making banking turns is ridiculous.

This idea of travelling in space being point your nose at where you want to go and burn until you get there is completely counter to how actual space travel works.

If you really want to get your head around how complicated trying to move things around in space is I suggest playing Kerbal Space Program.

Well a basic example of the problem with flying straight at your destination:

You have a space station in orbit over the Earth with a satellite in the same orbital path but about a mile behind.
If you wanted to dock the satellite with the station and pointed the satellite at the station and did a quick burn, adding a few feet per second of velocity to try and catch up, the satellite wouldn't get closer to the station, it'd actually get further away.

No, an object in orbit has a specific speed for that orbit. i.e. you cant have two objects in the same orbit going different speeds.
An orbit is really just a controlled fall where your forward momentum is so high that by the time you've fallen to the centre point of the earths gravity you're already past it.
An increase in velocity in the direction of travel would take you further from the earth and thus further from the orbit of the space station.
https://www.youtube.com/watch?v=QXOBe-CG4cw
In this video after the 7 min mark he has to have his ship and the target in two slightly different orbits to allow the target to catch up.

Another way of thinking of it is imagine a circular race track with multiple lanes. You have a car that when going at an exact speed (say 100mph) is unable to turn left any harder. If it is in the inside lane and it increases its speed to say 120mph it'll get forced into the next right hand lane for a bit allowing it to have a longer time to turn and then it can go back into the left lane for a bit but eventually that speed is going to be too much and it'll get forced back into the right hand lane.
A car staying in the centre lane is still going to orbit the track faster as it is on the inside and has less distance to travel.

Or, sit on one of those spinning office chairs, push yourself into a free spin and hold your legs out straight. with the momentum you have you might be spinning once every 2 seconds, then pull your legs in towards your body and you'll start spinning faster, maybe once per second. Same mechanic.

So, what you're saying is, those hybrid O.B.s do so much damage/have the largest AoE because they're about the size of your fist when they hit the ground :p

Inertia

The most important thing for ship speeds and maneouvrability would be thrust to mass ratio.
It'd be entirely possible for a larger ship to go faster than a smaller ship - if more of it, proportionally, was given over to engines than in the smaller ship.

Kind of relevant

I suggest zooming out a bit and turning on milestones and show paths. Keep in mind that everytime the Rosetta passes a planet it gets a gravity assisted speed boost. They launched it in March of 2004 only for it to finally catch up to the Comet in 2014.

BAMF

Given our technological ability that is an extremely awesome feat and will surely pave the way to bigger an better things.

I'm pretty sure it's controlled by computers.

It's an absolutely stunning work of calculation. Calculating the motion of objects being affected by several bodies that are affecting each other is insanely complicated and this level of precision is mind boggling.

Imagine throwing a knife out of a window, having it bounce several times and then perfectly cut a fly in two.
That's less precise than this.

Also I forgot to mention for the OP.

It depends on your definition of "quickest."

Lets say you have two ships that weigh the same. One has a fuel burning engine that produces 10,000 pounds of thrust and has 200 seconds of fuel. And the other has a highly efficient ion engine producing 50 pounds of thrust but can keep going for 48 hours.

1st one can change course quickly etc, the other can attain a higher top speed and can produce more thrust over all.

Yeah, this is why space junk is such a problem. It's ridiculously lethal if you're unlucky enough to hit some. There are some tiny pieces scattered all around orbit and if a piece the size of a fingernail collided with, say, the ISS, it would be as damaging as a grenade.



Well, theoretically, if it could be done.