I've two air impact wrenches. The one I pick up first is my old Clarke which I bought from Machine Mart many years ago and it's fine for run of the mill wheel nuts etc. It's a Clarke 07G - which these days seem to be this one:
https://www.machinemart.co.uk/p/cat23b-1-2in-square-drive-air-impact-wre/ When the going gets tough I reach for "The Hooligan" which is a C.P. 7748:
https://www.midlandairtools.co.uk/CP7748-chicago-pneumatic-1-2-impact-wrench and seems to align very nicely with the power you quote above for the battery tools - a wee bit cheaper too. Of course it does need a reasonably "meaty" compressor and I bought a 3HP single phase belt driven jobbie which sits on a 90 litre air receiver running at 125PSI That's regulated at 90 psi for the tools and the shop runs a 1/2" hose feeding a 3/8" flex hose to the power tool. The compressor is rated at 14CFM which means it's probably around 10, or a bit more, CFM free air delivery. Whatever, it allows the CP to absolutely laugh at wheel nuts and whips off drive flange nuts with hardly a pause. I'd love to try it on a Honda crank pulley nut - which have a notorious reputation for being almost "undooable". I'd be very surprised if it couldn't manage one.
All of the above is what makes air tools not a very attractive prospect.
If you're just starting out it can be a lot to work out, what compressor you are going to need to run what tools and what performance to expect. Then you need air lines which on their own can be quite expensive, then you have to make sure all your connectors are matching, do you need a line oiler or do the tools have oiling ports,
Finally the one thing no one seems to remember is to drain the tank, which on a nice hot summer day will accumulate quite a lot of water, which when left rots the tank from the unpainted inside.
Running a whole compressor, airlines and anything else needed to keep them in good working order becomes a massive headache if its all to run one impact driver.
I have to confess I did have an impact driver and compressor, the driver was an Aldi device which was actually reasonably good. My compressor was an aging 2hp unit which struggled to keep up with the driver. They took up a huge amount of space in the shed and I maybe used them 2 - 3 times total because by the time I had got everything out, set up and the tank up to pressure, i could have taken the bolts out of what ever the target job was, with a spanner or socket set.
So I sold them to my dad along with some paint guns tire inflator and a simple airgun/blower.
I may get a smaller compressor at some point for blowing dust out or to run a small paint gun, but its a lot of kit to commit to for a couple of air tools.
Basically the story is we are completing on a new house hopefully in the next couple of weeks and I will actually have a garage I can work in. There are quite a few jobs to do around the house and so getting tools which have an interchangeable battery both for automotive and for DIY and woodwork is going to be a bonus. I have corded jigsaws, drills and sanders, but having a battery sander for a job or a circular saw which doesn't have me trailing an extension lead across the garden would be handy.
Having a decent impact driver that I can just pick up and use on the car when needed without having to run a compressor up to pressure, would also be a god send.
I am very particular about organizing tools, it comes from being in a big family and everything always going missing so I am always very careful how I store and organize tools, With a garage I can use I am looking forward to building some storage solutions to keep everything neat and in its place.