George,
Golf is a game of how many. To the best of my knowledge, you don't get style points or degree of difficulty bonuses from the Russian judges.
If you shoot 90 in a medal tournament, you beat those who shot 91 and above, no matter how more artful their rounds were. In match, you can top a drive and skull a 5 iron into the hole and beat a guy who flirted with a hazard with his 300 yard drive to the ideal spot, then feathered a 9-iron to 3'. Every time.
Perhaps you may have enjoyed your 90 more than the guy who shot 70. However, you will not hear in the bar that George really had a good time, even if the game is for many of us exactly about that. Now, if I shoot 70, you will definitely hear about it, for weeks, incessantly.
In regards to your hypothetical, of course nearly everyone here would go for #2. I suspect that the best players in competition would choose #1. However, it is seldom a simple choice of one or the other.
I haven't thought much about it, but it seems that most holes have an ideal line of attack (maybe Behr's line of instinct). Varying from this line poses certain other risks and potential rewards. It may be rough, bunkers, trees, and even water in your #1 courses, or uneven lies, blindness, poor angles to certain spots on the green in #2. The challenges may be different, but they are challenges of shotmaking nonetheless.
If you are asking would I prefer to play Firestone-South or Cuscowilla, my choice is rather simple, Cusco, the #2 example. But in other cases, I may prefer Paa-ko Ridge (sp) which is more of your type 1 than Black Mesa (closer to a #2). I would wager that the really good players would go for Paa-ko. And who am I to say that the aerial game is somehow less meaningful for them, particularly if the objective is how many and not how.