The Carvin cab size is going to allow more low frequency extension (if you see the Epifani blurb they are talking about the classic 115 sound which is not about bass extension but midbass hump).
Either cab can depending on tuning and driver can give a big mid-bass hump. But the larger cab will do true lows better, and can be tailored for the amount of midbass hump with driver choice and tuning.
But realize I consider a three-way design to be a superior sound (for me) than say a 210 and a 115 running full-range. If I was using a 115 cab and another today< i'd be using an active crossover with one cab doing mids and highs, the other doing lower mids and lows. Which is what you find the LS1503 doing: the 15 handles 500 Hz and lower, and then the midrange driver and excellent tweeter/horn take over.