If such a thing did exist, I would be VERY interested...as long as the price was right. (not only am I cheap, I'm poor to boot)
Comes with a mic to measure your room & speakers and works its magic from there.
Speaking of Room/Speaker response equalization, although not automatic, there are ways to do this fairly easily and inexpensively with a few readily available tools (generally cheap and automatic are mutually exclusive). Bang for the Buck has always been a mantra of mine, and being handy, DIY (granted its not always cheaper) solutions like Room EQ wizard(computer based) or Audio Tool (Android) and an inexpensive Dayton measurement mic (that comes with its own calibration chart), and an appropriate piece of equalization software (ie VST plugin that works with many software audio players), can do a pretty good job.
From a Headphone perspective, it gets tricky.. Do you really want to put a microphone in your ear canal(as near the eardrum as possible) to measure the response of your headphones? I believe in the old line "Never put anything smaller than your elbow in your ear." Goldenears.net has a product that they claim can make any headphone (in their 800 headphone database) sound like any other headphone, but it only takes frequency response into account, notwithstanding transient response and other important aspects as to why any transducer sounds like it does. (a dynamic device is never going to sound exactly like an elecrostat or ortho, even if the freq response is the same) It's also not obvious from their web site how much their products cost or where to buy them. There is another company that will sell you a VST that provides the equalization to match your particular headphone to their "target response curve" that compensates for the gain of our ear canal, head etc, but unless your headphone is already in their database, you have to ship your headphones to them to have them measured so that they can create the compensation curve.
A third(free) option is to equalize your headphones according to your own hearing, using a fairly complicated process, and use any of the various VST equalizers to create the proper compensation. Being cheap and Lazy, I decided to go with a fourth option.
Tyll Hertsens over at Innerfidelity wants to create a database of headphone frequency responses, and has started with the measurements that he has done on headphones that he has tested/reviewed and also has a volunteer program where he will measure your headphones, if they are not already on the list. The caveat is that he only does it for US based people, likely to keep his costs(and complications of Customs) down (he pays for shipping both ways, so the cost to do it for the owner is ZERO). Being that I live fairly close to a US town that I can ship/receive to, I was able to take advantage of his service, and plan to use his raw measurements, and the Harman Target Response curve to come up with the compensation to be applied by an equalizer to create what should be the ideal frequency response curve for my headphones. Tyll has a blog post about this on IF.
In theory, if you know what the frequency response of your headphones and the target headphones, then you could create your own compensation curve to make yours sound like the target headphones.