I don't get militant like some people around here. I've never had much luck with mixing cabs personally, but I have no doubt that it can work with great results. The first time I ever got to play a mixed stack a long time ago, it was a 410 and 115 from the same company in the same line. I had seen many famous players do that, so I was pumped to try it. I was extremely disappointed, and noticed what has been said around here countless times, the 115 couldn't keep up with the power handling of the 410. The mixed scenario where I noticed the most audible phasing issues was with a 210/115 rig from the same company. Either cab sounded much better individually. I don't think there's really a rule of thumb you could go by, like a 210/115 being better than a 410/115, unless you're only talking about matching power handling between cabs.
There's basically 2 reasons people suggest not mixing cabs: power handling and phasing. The power handling thing is probably easier to understand for a lot of people. I was attempting to illustrate what is meant when people talk about phase problems. A lot of people probably don't even understand what phase is.
The 1-15 tuned low in my example was not even a bass cab, rather it was more of a "theater sub". I used it in the example because it and the 410 example were at two extremes. The more realistic example would probably be to show two completely different 410 cabs. The two 115 cabs in my example would be another more realistic case of bad phasing because I actually built and tested those two cabs together as part of an experiment. I was able to get them to play nicely together using a lot of processing (filtering and time alignment).
I don't think I'm the greatest player ever by any means, but I like to think I have a good live sound. A lot of bass players, many times players who are more skilled technically, ask me for advice on how they can sound like me live. In almost every case, they are running mixed cabs and are thrilled when I show them that they sound better live with a single cab that's better than their mixed cabs. The last player, for example, was running an Eden 410 with an SWR 410. He had way better results with a single 212. He and the band agreed that he never sounded better live as with the single cab. He had been running at much higher volume to make up for the "holes" in his frequency response with the mixed setup, so he was way too loud on some notes and not audible on other notes. He was able to have much more clarity at a lower volume with the single cab. Another case was a teenager in a progressive metal band. They were a great band with great songs, but their live sound needed serious work. He was running three different cabs (115/210/410 if I recall) because he thought more cabs would be cool. I set him up with a single 412 cab--massive improvement.
I will close with this, just like I was extremely let down by the epic 410/115 combo, I was extremely taken aback at the awesomeness of two high quality, matched 410 cabs the first time I ever tried it.