I would say a few things factor in:
As you mentioned, the number of games the average covers.
How low both averages are if both are lower but the same number of pins apart, more chance of a larger swing.
How easy the lane condition is on that given night. The easier the condition, the more likely for the lower ave bowler to "get lucky".

being on both sides of this lol....  I too was once the low 180's avg guy who could pop out a nice 650+ series..  And back then alot of it just depended on how well I was throwing the ball.   Not so much the lane conditions.  

But now being the low 200avg guy, I'll have times where I could be throwing the ball well and not carry and the 180's guy who is just tossing it up the track is carrying everything, and just smokes me.    Or I could get into a funk and just get a crappy reaction from my equipment or w/e and just struggle to get to the pocket.  

So on a THS, 90% of the time it's all about who gets to the pocket "better"  

On a tougher shot, most of the time it will favor the higher average bowler...  

This opinion is for scratch...

If your adding in handicap, I honestly think it's probably a 45/55 split on who wins for the nite.  Only cuz your 180avg gets alot more handicap and if he strings a few strikes that 220game scratch, turns into 250 w/handicap...

I know that just from experience lol...
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Handicap was never intended to be part of the equation.  What really got me thinking about this was one night in league we got 'schooled' by a team with an average barely over 900 (5 man team) that shot no less than 1,050 per game.  Our team average is over 1,000, but we had no response for the 180 average bowlers shooting over 650 and 700.