Joe,
It's not quite as simple as that.
One has to remember that golfers SHOULD play from tees commensurate with their abilities.
In addition, the higher the handicap, the greater the margins for error, which should be factored into each shot prior to execution.
Lastly, higher handicaps, while they aspire to score well, don't, relative to par. So, a good drive, leaving the high handicapper with an 8 iron into a green, that is hit "marginally" for a good player but, "standard" for the high handicapper will result in the likelihood of a bogey, whereas the low handicap still possesses the skills to recover his par.
It's not that the high handicapper can't hit a great recovery or sink a good putt, but, if he plays true to his handicap, the odds are against it.
See, see the ball Joe, be, be the ball Joe.