I couldn't play the old version for the life of me. But I am loving this version.
In contrast to Shapu's style, I never adjust my arrow unless there are balloons (and occasionly for the punchbag).
The way in which I play:
Shots without balloons:
1. Don't move arrow, only adjust power - close shots power is just under 1/2 (just before the arrow tip), middle distance shots is 1/2 power (on the arrow tip) and long distance shots are just over 1/2 (just over the arrow tip). I have never needed much more power.
2. Save powerups until last shot.
3. If I have it, I always use the reverse bullseye (blue) powerup and slightly raise arrow to hit the board for a Bullseye and another 3 shots.
Shots with balloons:
1. Angle arrow up slightly and use 1/2 power or less, so after you hit the balloon the arrow falls into the target.
With Punchbag Bob, try to keep power under 1/2 or under, usually any more will send it straight past.
My highest score is 166 and managed the bronze medal. I still have a long way to go before reaching silver or gold.
I hope that between our different styles, you will find a way that suits you, Anjuna.
EDIT:
New Highscore of 230!!