Probably the same as however battle arena xp was calculated before. Numbers don't look any different, as far as I recall.
I'm up to 47 and I'd say probably 99.9% of my xp going from 40 to here has been from the xp gained from daily missions. (Had been caught up with story before the update so there hasn't yet been any new story xp to gain.) Battles contribute next to nothing.
Old game design seemed to be built around
1) really difficult to obtain girls (which was a common source for player irritation)
2) fairly easy to build affection levels (only needed to stockpile rare lingerie, all else was unnecessary)
3) kind of difficult, but manageable (pachinko was a great source for extra items), to give girls enough xp to level up (every single item you could stockpile was useful)
New game design seems to be built around
1) fairly easy to obtain new girls (I know I've also gotten a couple to drop)
2) really difficult to build affection levels, or at least it gets there a couple dozen or so girls into the game (see all the concerns in this thread about the scaling requirements and costs (and pachinko scales too and all item sell prices are down, making pachinko a lot more of a risk now))
3) really really easy to give girls enough xp to level up (a single common magazine or book (4 or 9 xp) always seems to be enough for each new level, all else is overdoing it)