I choose action cameras as my go-to for on-car camera shots. It boils down to physics and economics. Action cameras are quite a bit less expensive than more 'professional' cameras so I can afford to mount more than one on the car at a time, meaning multiple angles per run. An added benefit is that smaller, lighter cameras require less mounting and rigging - another major time saver. I can also testify through experience that if an action camera falls off it tends to bounce rather than shatter. While nowhere near as good as cameras with professional lenses and sensors, modern action cameras can still have really nice footage coaxed out of them, especially in good lighting conditions.
Image: Classic Motor Films
Here's a run-down of the specs that really count, and the nice to haves. If you want specific brand and model recommendations, skip to the end. If you have an action camera a few years old, its worth checking to see if it supports these capabilities.
Until just a couple of years ago I would have said you can get by with 1080p resolution. Even though most films are produced in 1080p, 4K sensors capture much better quality video and give the film maker the flexibility to zoom and pan within a shot. You can see how much more information a 4K sensor is able capture relative to older technology.
If your camera translates every lurch or vibration you will be hard pressed to get usable footage from a moving vehicle. Such effects can sometimes be used quite artistically, but for the most part your camera should be capable of smoothing out sudden changes of direction. This is where sensor resolution is your friend. A 4K sensor has enough space to accommodate a stabilized 2.7K frame. The action may be flying all over the sensor, but the 2.7K frame can be moved to make each frame appear to be a smooth transition from the previous one.
Image: Classic Motor Films
24 or 30 Frames Per Second (FPS)?
There's no wrong choice here. When I'm combining footage from a lot of different cameras I will set mine to 30 fps, which is generally the default for action cameras. It means that the look of the footage will match more closely. If I'm exclusively using my own cameras I will use 24 fps, which makes the result look a bit more like film. This setting also allows the camera to increase the bit-rate or amount of data captured per frame.
Exposure Control Of Some Kind
A large part of the 'choppy' nature of action camera footage is down to their tendency to shoot the fastest exposure possible. This tends to eliminate motion blur and even stop action such as rotating wheels and propellors, even waving arms. If your camera allows you to set a maximum ISO, you can use this to force it to take longer exposures - which can also coax better image quality out of the sensor. I have found ISO 800 to be good compromise. If your camera has a means to directly set exposure, using 1/50 of a second will produce much more natural motion blur, but you will almost certainly need to use an ND filter.
Image Quality Control
Action cameras off the shelf are designed to create footage that you can share on social media. Generally, colors and sharpness are artificially boosted to give the illusion of detail and clarity. In reality a lot of the information being captured by the sensor is being destroyed. Settings for a Flat Color Profile and to turn Sharpness to Low or Off give you the flexibility to finely control both of these in your editing program.
Field Of View (FOV) Control
It's a nice to have, but the ability to set a less distorted capture will save time when you come to edit, and I think in-camera distortion correction works better than editor plug-ins. I always use Linear FOV.
Over the years I have followed the evolution of the GoPro range of cameras, and while there are challenges from DJI and a number of others, GoPro has consistently delivered the best video quality and stabilization. I also find them to be rugged and tolerant of abuse.
I find even my Hero 5 Black to be still quite usable, but would absolutely upgrade from anything older. The Hero 6 Black was a nice step up in image stabilization and is still in regular use alongside my Hero 7 Black.
I would steer clear of the GoPro Session cameras - they are finicky to use. The Silver Editions have always been cheaper, but their image stabilization isn't so great and they lack a Linear Mode.
The Hero 7 Black, like each generation before it has slightly better dynamic range and image stabilization, and is currently my primary camera.
The Hero 8 Black is on my list to purchase. Its stabilization and picture quality are even better, and it's the one to get if you are purchasing now. If you are on a bit of a budget the Hero 7 Black is still being sold. Either camera should last you years.
From time to time GoPro offer a generous trade-in discount. As I write, it's running one right now. Send them any old digital camera - including an older GoPro and get $100 off a Hero 8 Black or $50 off a Hero 7 Black. https://gopro.com/en/us/shop/tradeup
In the meantime I'm looking at the latest crop 360 degree cameras. That's a whole other story.