Zadok_Allen: If levelling is presented as a story in itself and "opens a new chapter", distinct from combat, a full heal feels appropriate however. Such level ups are often presented in full screen, bring their own theme and do their best to have the player focus on nothing but levelling up for the time being. The story before and after are divided due to it already, so a full heal is a warm welcome to a new chapter and can't mess with flow.
Usually, I see the beginning of a new chapter not associated with leveling, but rather associated with things like the following:
* Completing a dungeon, or defeating an isolated boss (an isolated boss is a boss that isn't attached to a dungeon); similarly, in stage-based games, completing the stage (Castlevania 1 is the sort of example I'm thinking of for a stage-based game)
* For story-oriented games, a major storyline event occurring
* Similarly, when the game changes its point of view to another party entirely (Dragon Quest 4 is a good example here, Final Fantasy 6 does this at one point, but FF6's multi-party battles and dungeons don't count here)
* For quest-oriented games, completing a quest
* Perhaps, in games with expensive class changes, a class change. (So, for example, Wizardry series, Dragon Quest 3, ant AD&D based game that allows dual classing, but not Final Fantasy 3/5 or Dragon Quest 6/7.) That might be the only one related to character growth that I'd really count.
* Also, I think being able to get a full restore in town or another safe place makes sense. (I actually don't like how many WRPGs subvert this by letting you rest anywhere except in town; why have that restriction?)
In any case, I don't see leveling up to be the start of a new chapter, but just a minor evolution in the character's abilities.
(Also, note that there are games that don't use levels and instead have more granular character growth, like most SaGa games. Then again, many SaGa games give you full HP (not LP) for every battle.)
Zadok_Allen: B) If You have distinct combat and levelling, so You'd only level after combat is concluded, You should get fully healed.
That can still break resource management in longer dungeons, where part of the challenge is managing your resources so you don't burn out before the end of the dungeon, or you at least have enough resources to return to town when you start running low.
(Sidenote: I don't like it when games take away the option of returning to town.)