Granted, I don't know how this works in Squadrons, but typically what you have is the input delta being mapped to the acceleration of the ship along a given axis.
In the case of a joystick (and also an analogue stick, because for all intents and purposes they are the same thing in this context) your offset from the center determines the speed of rotation (Or, determines the acceleration of that rotation, up to a pre-defined maximum). In the case of a mouse, because it has no "offset" that rate of change is mapped to the delta-position of the mouse.
This means that in order to have a constant velocity turn, in the case of a joystick you simply hold the joystick in a given direction. In the case of the mouse you have to make a constant motion (including moving the mouse "back" when you reach the edge of your surface). Already you can see that there's a difference in terms of required input here (As to which you think is better for you is a matter of personal preference)
Moving onto aiming, obviously when working with a mouse the physical area that you have to work with, as well as how that physical area maps to the produced game-input is significantly more tunable than when working with joysticks. Yes, stick sensitivity can be adjusted but it has no impact on the upper extents of how far the stick can move from the origin. In general though, it means that fine-tuned movements are much easier to produce with a mouse because you can lower the sensitivity and have a much larger area to work with.
In typical (as in, semi-realisitc) dogfighting scenarios Joysticks may end up having the upper hand due to not needing to be "rest" in order to continue rotation, however in a game such as this I can almost guarantee that a typical dogfight will not be the meta (especially considering that drifting is an option and lateral thrusters are included) and that a more twitchy-based approach which lends itself to short, accurate changes in orientation.
I'm going to post a video here from Planetside 2 (Which I played, and piloted in for many years). The air-combat meta in that game evolved into a kind of "hover-duel" which involved craft facing off against each other, and essentially maintaining orbit with each other whilst trying to simultaneously lead their shots and dodge the enemy's. Now, I have absolutely no idea if something similar will develop in squadrons due to there being entirely different world-physics going on, but PS2's aircraft also are operated based on the "axis-acceleration" model (rather than direct mapping of inputs) so in terms of control input, the games seem similar.
(Warning: Music is a bit loud)
As you can see there, the combat is less about trying to out-maneuver the opponent and get behind them (Like in realistic dogfighting games) but more about making small, twitchy movements which lend themselves to mouse control much more than stick.
We'll have to see how things turn out though, I always love discovering new metas :)