larger diameter speakers tend to have a "boomier" sound. its not necessarily better or worse.. its personal preference. there have been quite a few nice cabs built around a 1x15 or 2x15 configuration. some old SUNN cabs come to mind. they sounded pretty good.
Most 15" bass speakers with 1/2" cone dispersion cut off around 2khz and require a added horn for high end, which I use with a switch to disable the horn for added effect, and I know alot hate the horns. I just use this for bedroom playing for low wattage amps that usually are equipped with 6" to 10" speakers that don't have a wide response. If you want a serious 15" for gigs or rehearsal look for a 15" guitar speaker that doesn't have 1/2" cone dispersion. I use a JBL D130F that can't be used for bass or keys.
im not a big fan of 15 inch speakers for either bass or guitar. my experience is that they get too boomey. 12 is ideal for my guitar use and i like 10s for bass. note that with my style i like my sound to be very tight with both guitar and bass. i would try a 15" inch for real drop tuned stuff, or for a smoother sound.
once again i like my sound to be very tight. follow your ear, your mileage WILL vary.
I'm a big fan of 15" speakers for guitar. 3 of my amps are 1x15. Two tweed pro types, and an Ampeg Gemini II. These speakers are slower reacting than the smaller ones. That's certainly true. The other negatives mentioned are hard for me to relate to, as I've not experienced any boominess or difficulty driving such amps at lower volumes.
Emi Big Ben: ceramic, big bass, LOUD. way better loud than quiet. Rips and roars.
Emi Legend 151: ceramic, big bass, LOUD. Extremely balanced, smooth. A rather vintage tone. Just as good quiet as loud.
Weber Cali paperdome ceramic: Nothing JBL like about it. Warm, soft edge with muscle underneath. Where the big ben roars, this one howls.
those are the current faves. You don't get more low end with 15s in my experience. You get a very different mids and highs. Highs especially.