Most automation can be detected now. Distil networks and many others detect selenium and phantom through js and header analysis. Having said that you'll probably find whatever you're planning on automating will ban you based on activity rather than browser/software.
Phantom is easy to detect, there are a lot of details online of how to do it. It uses / or used a very old version of webkit and the headers were sent in a unique way.
Also you could crash the JS and get phantomjs strings, you could detect specific JS properties.
Firefox / chrome on the other hand use the INSTALLED browser on your machine. So headers are sent exactly as the browser. selenium firefox = normal firefox.
As for JS detection, I am not aware of any. There are no exposable selenium JS code to detect, so I don't think it is as easy as it is made out to be above. I would guess someone is passing on 2nd hand information as opposed to personal experience.
But as stated some companies are detecting selenium with a high probabilty. Distil being one of them. I read about this briefly and no one is really sure. They talk of taking a finger print of the browser and behaviour. Perhaps timings, perhaps JS events. When you call a mouse event in JS, did you trigger of other mouse events expected to occur before?
If your mouse clicks a button, there should be lots of DOM enter / exit / hover events. Could be a metric. Bypassable by automating a real mouse though
However, perhaps is possible but certainly is not simple that every one and their grandma knows. That is false - until I am shown evidence to the contary.
For automation of a browser your best bet is still selenium with firefox / chrome.