IMHO opinion it is way past time for people to forget the silly idea that smaller spaceships are either faster or more nimble than larger spaceships.
Why? That's exactly the way it works in the REAL WORLD. It's not a stretch to imagine it would be the same for science-fiction vessels.
Suppose that space ship A has dimensions B, volume of B cubed and mass C. Suppose that Space ship D has dimensions of 2 B and thus a volume of 8 times B cubed and mass of eight times C. If the engine of space ship D has twice the dimensions and 8 times the volume and mass of the engine of space ship A, the engine power of space ship A and space ship D should be the same proportional to their relative mass...
It's not. In conventional rocketry, engine power doesn't scale in a linear relationship with the size of the engine. Because of the increased mass of propellant and tanking to maintain a ratio of engine size, the engine must also be eight times as powerful to have the same acceleration and also 8 times the propellant to have the same Delta-V.
This can be achieved by simply adding eight times as many engines to the larger ship as the larger one. The new engine wouldn't be
proportionately larger, since the engine structure is only increasing size in a single dimension (along the rear surface of the craft) and not getting longer as well. So the larger vessel will have the same performance as the smaller one with a proportionately smaller engine.
The real problem is, as I said, engine power doesn't really scale with size. The old rocketdyne J-2 engine was actually LARGER than the SSME used on the space shuttle despite the fact that it produced about half as much thrust, the modern Merlin rocket engine produces about half the thrust of the old J-2 engine despite being LESS than half its size and one-third its weight. And then there's the RD-180, which produces about 4 times the thrust of the J2 while being almost the same size but also 4 times heavier. So it's entirely possible that adding an engine twice as large in every dimension as the previous design would result in a tenfold or twentyfold increase in thrust, or -- depending on the design -- only double thrust and require you to add a lot more of them than you normally would.
So there's two factors to this:
1) A ship that is twice as large won't actually BE 8 times as heavy, in fact it's likely that a vessel 8 times as massive would simply be eight times as large (take eight spacecraft of identical size and bolt them all together). A good example of this is the Apollo and Soyuz spcecraft: Apollo's CSM is is 4 meters wide and 11 meters long, where the Soyuz is about 2 and a half meters wide and 7 meters long. Even ignoring the fact that more of Apollo's internal space is machinery, the CSM is about 4 times the volume of the Soyuz-TMA. Except the unfueled Apollo CSM weighs about 11 tons, while the unfueled Soyuz weighs just a little under 7 tons. So you can actually get a massive increase in spacecraft size for relatively little weight; Incidentally, Apollo also manages to carry about 18 times as much propellant as the Soyuz, which, combined with a larger engine, gives it better acceleration and better delta-V.
2) Engine power doesn't scale with size, and it's possible for a very small engine to have more power than a larger one if it is engineered correctly. More powerful engines do tend to be HEAVIER, but they don't tend to be BIGGER in terms of actual dimensions.
In space there is no resistance from the vacuum and the higher powered large space ships are faster and more maneuverable than he smaller ones.
This is unlikely, since a space craft doesn't actually have to BE larger in order to carry a more powerful engine, or for that matter, more propellant. This is the other problem with your analysis: maximum acceleration is less important than total delta-v, and a spacecraft that can reach a higher maximum velocity is actually more useful than one that can reach a slower velocity more quickly.