It's funny to me how all the "science crusaders" in these threads almost universally manage to miss the forest through the trees. Funnily enough, the same usual suspects usually pop in and focus on one or 2 issues a piece, and being adamant that these things mean you ABSOLUTELY CANNOT EVER take a particular course of action, while neglecting many other factors that don't support what they are saying.
I'm all about the science, but music making is a mix of art and science, and you have to know how to balance the 2.
1) If you're going to use "full range" cabs either way, there isn't really any downside to using 1 for lows and one for highs.
2) Considering a decent single 15 (rated say 300w or higher) is enough for a wide variety of applications all by itself, using it JUST for lows, while using another cab for mids and highs is JUST FINE. The other side of this is that if you have a 1x15 and a 4x10 and you want to do this (bi-amping), you most likely should use whichever cab has the lowest frequency response. So if you had a modern, high power 4x10 that went down to say 38Hz and an older vintage 15 that only went down to say 60 and had much lower power handling, it would make more sense to "flip" the traditional roles. However if the 4x10 has a tweeter and the 1x15 doesnt and is also modern and high power handling, the high end may end up being more important than the last few Hz of response in the overall sound if that is the case. You just have to experiment and see what works best.
3) There's nothing wrong with "under" using a cab. In fact, that should be the normal mode of operation. If you have a 400w cab and you only put 100w to it most of the time, that's great and the cab will probably last you forever and a half.
4) If you can't hear when a speaker (ANY of your speakers) is having trouble keeping up, you need to spend more time with each piece of gear individually, getting familiar with it's limits, so that you can recognize when to back off.
5) While a 4x10 will often have higher power handling than a 15, with 2 cabs, your power output gets split in half anyway, so it may not even be an issue, it might just mean that your 4x10 has a bit more headroom than the 15, but who cares? It only matters if you frequently find yourself running balls out and not having enough volume. But in most situations with a modestly powered amp (300-500w or so) and a couple of modern spec'd cabs, this is fairly unlikely unless you play in an exceptionally loud band.
For the OP, it really depends on what you are trying to get out of your rig that you aren't now for what you should do to move forward. Since you have a certain set of gear now, I would try all the different options available with it before jumping straight to purchasing new stuff.
THEN, if that does not yield a satisfactory result, I would probably just sell both cabs and get 2 that pair well together (whatever that may mean to your ears). 2 cabs of the same series is usually a safe bet. Different manufacturers will tend to have different "voices" so certainly combining them could be unpredictable. But who knows, right now my practice setup is a modern Trace head, vintage Trace 2x10 (no tweeter), and a vintage Carvin 1x15 from the 80s with a "vintage modern" JBL driver (M-151, primarily used in the Ampeg Gene Simmons cab I think). And it all sounds pretty damn awesome together, either with my Kramer aluminum neck, or the Carvin LB70P that I'm borrowing.
So the moral of the story is, listen to the advice you get here, but take all/most of it with a grain of salt and go out and try things for yourself.