The ATH-40X headphones are a step down from the ATH-50X, but still very good for me. Another plus for them versus others I have is the cord is detachable which is often the first thing to break, so it can be replaced if needed. Two cords (one coiled and one straight) come with it that have the smaller plug stereo tip and the screw-on larger adapter tip. I also got a storage pouch with it. They seemed to have a good balanced sound overall with a small boost in the lows and another smaller one in mid high frequencies to my ears.
The Sony’s seem to also have a small bass boost with a small low mid dip and slight push in the highs to me. Warren Huart did a nice YT vid (Produce like the Pros) on them that should be easy to find and Andrew Scheps is also a big fan of them. In several YT vids, he says he mixes in the box primarily now and only uses them. Andrew and Fab DuPont also did a recent free vid discussing headphones on a pure mix site that is interesting (google search - you may need to register?). In several YTs, Andrew puts into context why he uses Sony MDR-7506 headphones, saying that he got used to them in relation to what happens in a mix and how a mix sounds with most types of speakers then. In essence, he adapted to them over the years. He also adds he doesn’t use any corrective software to flatten the frequency responses. His advice goes along with the “just get use to what you got” train of thought.
That said, I have been trying corrective headphone EQ response plugins as mentioned in an earlier (well said) post here as well, like Sonarworks and DSoniq, with some good results. I also tried virtual room headphone plugins like Waves (NX and Ocean Way Nashville, but didn’t try Abbey Roads which Warren Huart also says sounds realistic to him in another YT vid) and others. I find that the corrective headphone software does make both headphones (and my open back AKG-K240 Studio headphones) more EQ flat, so closer to each other.
Also it is important to consider some other factors, such as that even the same headphone models can have differences, which is why some companies have a calibration service for your specific headphones. Adding to that, there are differences in head shapes, ear sizes and canals, etc that affect sound and fit. All this makes “best” headphone recommendations often more what works best for me and not for someone else. If you can demo headphones at a music store nearby (not always easy to do these days), that may be helpful.
I have read a lot (pro and con) about corrective headphone software. As I said, I am still experimenting with or without it. It seems one common thread is often that the trick seems to be pick one method, though, and get use to it without switching (between headphones or using/not using corrective software) which was also good advice in an earlier post here I believe. So +1
on that. Good luck! 
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