Sometimes wargamers talk about this as two opposed sets of elements. In the red corner, "war": history, accuracy, realism, simulation, detail, serious. In the blue corner, "game": contest, competition, entertainment, excitement, fun. But within those two sets there are obvious tensions. A dour tournament contest/competition can be at the expense of excitement/fun. Disproportionate obsession with detail can detract from the overall simulation (think of the (in)famous boardgame, Campaign for North Africa). History doesn't have to be serious.
So I think it is actually more like a triangle than a simple spectrum between two extremes. The three corners are military history, game mechanics, and winning/losing. Or more abstractly: context, process and result. Most wargames combine all three in differing degrees. The relative importance of these major ingredients determines where a game sits in the triangle.
At our club there are usually three different groups, each exemplifying a different corner of the triangle. Half of the hall is taken up by tournament games where - to characterise simply - history is largely irrelevant, game mechanics are deliberately fiddly and laborious, and result is everything. (Don't get me wrong - they're good people, and we wouldn't have a club without them - it's just not my thing.)
Then in the corner nearest the door is a fun group with eclectic tastes in games. They might do a big ACW or WWII battle one week, some medieval skirmish the next, and the week after that could be dwarves vs lizardmen or competing ants' nests. There the emphasis is on fast, clean, fun game mechanics - usually with rules that use squares, so no measuring and no arguing - and it is first and foremost a game. Those boys have fun!
And in the other corner you will find the BBB games. These are geared towards producing a result, of course, and the rules are sufficiently swift and simple to enable that. But what distinguishes our corner from the others - for better or worse, all a matter of taste, etc - is the focus on history and on recreating actual battles.
Of course just because a particular game or type of game sits in one corner, that doesn't mean we as players can't stray across the boundaries. We want different things at different times. After an intense day of historical action at Historicon, a few drinks and a Western gunfight or pirates tavern brawl may be what's required.
Contrasting cases in point were our recent games. Our Waterloo at SOFO was a very serious affair, as close as we could get to a realistic portrayal of one of the most famous of all historical battles.
But then at the club, for light relief, we did something less historical and more generic: "Bzura Breakout". This was a WWII 6mm game set in Poland 1939 and used the Kampfgruppe Commander rules. Although it was based on a historical situation, we used an invented map. Forces, deployments and reinforcement schedules were based less on historical OBs and more on getting the interesting toys on the table. Thus the scenario was designed primarily to make for an open, free-wheeling game in which the situation would change every turn and generate maximum decisions, maximum swings of fortune and maximum fun. A bit of historical context, but nobody really minded who won - it was all about play. Happy warriors!