Running specific tones probably won't help you too much as already stated. However, I can tell you a couple things I do to A/B speakers and identify a variety of issues.
1. Run pink noise through speaker A and then speaker B. You can probably hear differences even in mono, but go to your listening position and compare in stereo too.
In my experience, whichever you think sounds better with pink noise will usually correspond to better sound when regular music is played.
It's not a scientific or full-proof method, but considering the primitive material some people use as "reference" tracks, it's no worse and makes it much harder for you to be fooled by biases or other things going on with more complex music (i.e trying to judge vocals, bass, soundstage, extension, sibilance, etc. all at the same time).
2. Leverage technology. I use Jriver as playback for digital material and there is an option under DSP playback to see an "Analyzer" on screen while the music plays. It will give you a good idea of the frequencies being reproduced and their "volume" relative to other frequencies.
You might ask.."How does that help me?"...Well, it first helps you from making inappropriate conclusions.
For example, I've had more than a few audiophile friends use a particular test track as their "reference". I was often surprised that they would sell certain high quality speakers that they said were too bass heavy, while cheaper monitors sounded better to them.
Come to find out...if you look at the material via the Analyzer, it SHOULD sound bass heavy at certain points. That's how it was recorded. The amount of sub 100hz material is double what is over 600 hz for most of the song.
A lot of what people pass around as "audiophile" recordings are not really good to use as a reference. They just sound good. A true "reference" requires something you can compare with in real life. Since most people aren't at the live studio recording, your best bet is to listen to acoustic music and/or leverage technology to at least give you data about how the original recording was mixed.
For those with ears that qualify for Mutant X-Man status, these tips are unnecessary. However, I've found them helpful.