There's nothing "wrong" at all with mixing different cabs. Sound reproduction, and MI amplification especially, is all about compromises. Frequency response, tone, power handling, sensitivity, these are just a few of the elements that come into play when building a system, not to mention cost, size, weight, and all the physical parameters that have to be dealt with.
Matching is "safer" yes, if you don't plan on listening to your setup before using it. Since most people do, "safety" is really a non-issue. As far as matching being cheaper, actually the reverse is true. A single great cab that can do everything is typically going to be more expensive than 2 pretty good cabs that both bring something different to the table. Out of my 4 bass cabs, really only one would be appropriate to use in a dual matching setup (a vintage Carvin with either a JBL or EV 15 in it), and I still like it better combined with my Trace 2x10 (which adds a bit more crispness to the highs). The 2x10 is a great cab, but the low end is a bit lacking for use on its own. But it slays with the matching Trace 15. But the Trace 15 by itself doesnt have the high end extension I want, and it weighs like 82 pounds and ONLY fits in the passenger seat of my car, so having 2 of them would not be practical. The other cab is a vintage 2x15 with low power handling (for now, until I replace the drivers with something more modern), and it sounds cool, but its definitely more for that vintage vibe with mainly low end rubbery thump and not that punchy, crisp, modern sound (and it's 4 ohms which makes it difficult to use with other cabs).
You might say, yeah, but for the cost of those 4 cabs, surely you could have 2 higher quality matching cabs that would do everything you would need? Maybe. But in fact I spent less $600 combined on all of them. They're kind of "misfits" (except the Trace pair, which to be honest are 22 years old and a bit road worn albeit awesome sounding) that I was able to pick up for great deals, here and there. I'm not sure I could find a better performing matching pair of cabs for $600 or less than what the 2x10 and either the Trace or Carvin 15 can do (unless I could get another Carvin cab and get a good deal on a NOS EVM 15B). And really, I want for nothing in terms of tone and volume. The Trace 15 has low end for days. You dont have to EQ it in, it's just there because of the cab size and design. So the 2x10 sits happily above it cranking out low mids on up. I mean, the Trace guys back in the day surely designed these cabs to be used together, and sorry, but I have a feeling those dudes are smarter than anyone in this thread, and they put out the legendary gear to prove it.
So use yours ears first, and then engage your brain if somethings not meshing right. obviously, it helps to make sure power handling, impedence, etc... are all appropriate.
Having said that, in this particular case, it might make most sense to go with another identical 1x12. There is something to be said for have 2 small cabs with decent power handling and frequency response. Also I personally don't like to mix consecutively sized drivers (ie 10 and 12 or 12 and 15). You're not as likely to get the common benefits of different sized speakers, the power handling and cone area aren't as likely to match up, and it just looks weird. But a 15/2x10 setup really can be a thing of beauty with the right cabs.
