I went with Law for this first run & let me tell you it was very hard to resist the temptation of killing every God damned enemy on every battle scenario, especially towards the later parts at around area 8 up to the end.
You see my main gripe with the game is that those damned AoE (Area of Effect or simply multi-targetting attack) mages do huge amounts of damage on my troops if I don't kill 'em first. Also, I don't know if it's a game bug, but I noticed there are instances when if you level up in battle your character that leveled up sometimes do not receive a stat boost, whereas if they do get a level up at the mission de-briefing screen (once you win a mission) they always do get stat boosts. This was very annoying because Shane (my Favorite Flying unit) had little HP towards the final battle.
Will I do another run on the opposite path you ask? Sure, at least that path is easier, just kill, kill, kill! LOL!
Gaining experience should be easier on Chaos since all I need to do is kill everything on sight