The "Why Not Both?" meme is more than a little overused when it comes to decisions between two good things, but it's the perfect answer to the question of whether you should use a controller or a mouse to play your favorite games.
The main problem is that keyboards are not analogue. A key is either depressed or it isn't. This makes it essentially impossible to implement manual movement control for games using a keyboard. You have a walking speed and a sprinting speed, with nothing in between, and a significant amount of imprecision as a result. That analog thumb stick on the controller lets you precisely control the velocity of your character, and it's intuitive.
However, as soon as you try and use that same type of thumb stick to aim, things go south quickly. When we look at something with our heads, we turn and snap to it. You don't slowly accelerate and decelerate your head, overshoot what you wanted to look at, and then turn back. However, that's exactly what happens with an analogue thumb stick, and it's why any console games that require precise and fast aiming come with "aim assist" which snaps your reticle to the target or otherwise fudges it when its close enough.
So we have two halves of a good control scheme, which brings us back to...
The idea is basic—use the left half of a console controller for movement of your character and your mouse for all the aiming. This lets you get the best movement scheme in total for your game. Sure, there will be a learning curve, but you'll get the hang of it quickly if you persevere.
However, you've probably already spotted one major flaw with this—a lack of buttons! With your left hand on the keyboard, you have access to numerous buttons beyond movement. With just a standard controller in your hands, you have movement, you can click the stick, and you have one trigger and one bumper. If you have a fancy controller with paddles, then you
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