If you go to the Sonarworks
site, they're currently offering a downloadable free guide that covers headphones for mixing and mastering. They've analyzed around 800 headphones in order to generate compensation curves, and chosen the ones they feel are the best. If you click on a headphone to read the associated review, you'll see the headphones' frequency response curve, as well as info about weight, durability, etc. The uneven response of most phones is scary, but at least you'll know what you're dealing with.
I have several sets of headphones. The true test of Reference 4 is I tried their compensation with multiple headphones, and they all ended up sounding pretty much the same in terms of response. However, be aware the frequency response curves are averages. Curves vary for different production runs and even models within the same run. If you really want to go down the rabbit hole, you can send Sonarworks your specific headphones. They'll do an analysis and provide a custom compensation curve.
The Sonarworks Reference 4 software that compensates for headphone anomalies is very cool, and doesn't cost as much as the version that can also tune your room for monitors (the headphone version is $99 IIRC). I highly recommend this software if you have to mix or master on headphones, but at least the guide will let you know what's wrong with your headphones (e.g., hyped bass, missing midrange, etc.), so you can compensate. You can even create a rough compensation curve with EQ based on the graphs.