It's simple: A 4x10 has almost 4x the surface area of 1x15. It moves more air, so it's MUCH louder. Your 4x10 drowns out the 1x15, making it pointless.
Yes, it is simple but not that simple. The standard saying is, "there's no replacement for displacement" and that's because displacement is what really matters. Displacement is the surface area times the excursion. The formula for the surface area is :
Surface Area = Π x (radius - surround)2
Typical speakers used for bass have a surround of between 0.75 and 1.0 inches. With a surround of 0.75, a 10-inch speaker will have a surface area of 56.7 in2. With a surround of 1.0, a 15-inch speaker will have a surface area of 132.7 in2. This means four 10s will have a total surface area of 226.8 in2. That is a factor of 1.7 times the surface area of one fifteen.
Then we have the excursion to consider and there is a very wide range of values for that. There are "Super 10s" that have excursion equal or greater than most 15s but the typical 10s found in 4x10 cabinets is considerably less. So much less that many 4x10 cabinets have a displacement about the same as typical 1x15 cabinets.
When many companies design their cabinets they try to make the sensitivity of the cabinets within a given series to be as close as possible. Here are some example of companies that have done this :
Hartke - Hx115 : 98, Hx410 : 99
Hartke - 115XL : 98, 410XL : 98
Hartke - AK115 : 98, AK410 : 98
Ampeg - PN-115HLF : 98, PN-410HLF : 98
Ampeg - SVT-15E : 98, SVT-410HE : 98
G-K - Neo115 : 99, Neo410 : 98
I could go on but I hope you get the point. Displacement and sensitivity don't tell the whole story though. What really matters is how the speakers sound together and that is highly subjective. One thing I often read is that 15s play deeper than 10s and that is just not always true. In many cases it is, especially for two cabinets in the same series, but it often is not true at all. In the cases of the speakers I listed above, the 15s do play a bit deeper than the corresponding 10s but there are many 4x10 cabinets that play very deep. The Ampeg SVT-410HLF is one example and Eden's 4x10 cabinets are another. The bottom line is that is not a good generalization to make because there are too many exceptions to consider it a rule.
As for the brigade, I am definitely not a member. I have heard this combination sound very good at times and I have also heard it sound bad, just as I have heard some identical cabinets sound bad. I will certainly not state that a 1x15 and a 4x10 cabinet can not possibly sound good as I have read many times but I can not state that it always sounds good either. One's bass and amplifier play a big role in your sound and some people can make practically anything sound good just as some can't make anything sound good, no matter what they do. You just have to use your ears and go with what YOU like or get the opinion of someone whose ears you trust.
.