I have had alot of experience with both, DD-15/DD-18 and ended up with the DD-18s each time.
I ALWAYS run subs in pairs. Aerial SW-12s, Velodyne F-1800R's, HGS-18's, HGS-18II's, DD-12's, DD-15's, and DD-18's. I had a pair of DD-18s, sold them to go back to the Aerial SW-12s.
Now, these are the only subs I like personally. The SW-12s did better at all volumes/material than did the HGS series of subs. I preferred the 15s over the 18s from the HGS series, as the 18s didn't have enough power to keep up with the driver, so it was slow and needed volume/room to 'catch up' to my mains, but was quickly overpowering even set at about 2. Then the DD series emerged. Again, I got into the 18's, and was shocked at the presence at low to mid level volumes and the spectrum they can cover. I know Velo told me they increased the output by 2DB, which normally isn't a big deal, but in subs it is a HUGE deal, and mid level volume is where I noticed it most. No, wait, maybe that was because I was finally able to dial in the room with the built in spectrum analyzer?
No wait, maybe it was the increased servo speed of the DD versus the HGS? No wait maybe the spectrum? No wait, maybe..........anyway, you get my view.
The change between the HGS and DD was a huge step. Now, 15 versus 18s? I doubt VERY much at normal / moderate listening levels anyone is to notice differences between the 15's and 18's. Anyone unless trained professionals with perfect rooms and ears. As you probably know, the room will change the sound more than anything else, so probably no reason to get hung up on the sound differences between these two at normal levels. My bet is they will act / sound the same.
The big differences kick in as the volume levels increase and you start to walk away from the mid-low bass of the 15s and start getting into the quick, deep push of an 18. There is nothing, imo, like a correctly powered 18" sub driver, actually 2, in a system for 2 channel. Just incredible. I have someone that has a full scale ORGAN (like 100ft tall, 200ft wide) that bought 2 DD-18s for reproduction of sound in the hall! And home theater, well, suffice it to say, if it is good for 2 channel, it is great for theater. I don't think there is a better sub for 2 channel or theater, low to high levels of output as the DD-18s. I definitely feel bass is directional, despite what many others say, and in stereo, dialed / spectrumed (is this a word?) in there is no better.
Alot of folks in the 18" game look into Bag End. They never had enough power for my liking, which led to weak/anemic tonal control of the driver. I am not a huge fan of ported subs, as the Aerial SW-12s are. The had to be to achieve volume but the mass air push on my legs during huge passages was quite annoying despite their nice presence at normal levels. Servo's of the DD series are so much more advanced than those of the HGS series (alot of hum, buzz, etc.) and seem to get bass right.
Now, again, this is all my experiences, my opinions, and you know what they all say about opinions? Like asshol_s, everybody has one. But, that being said, I am not a dealer, I don't 'represent' any lines, have no affiliates, and have had the ability to try / demo many subs (powered and not - passive like Snell 18's, JBL 18's, and some older Kinergetics) and have landed 100% into the DD line. If space (physically) isn't an issue, go 18's, you will not be disappointed!
For what is it worth, I am running 2 pair of JBL K2S9800SEs, matching center, Levinson 33's, Meridian 861/800 for theater, and the Conrad Johnson Premier 8A's and the CJ ART in 2 channel. Oh yeah, a trio of DD-18s, stereo pair in front, single in back (for theater - as if really needed).
Dan