I can see similarities between the two and the technological advances have similarly helped both average shooters and average golfers.
Golf used to be entirely a game of feel with the technological advances only being in the clubs. Wood shafts and heads at first, then steel shafts and heads, then graphite shafts, then titanium heads, then the USGA imposing a limit on a club's MOI. Add in the use of a laser range finder, or using GPS on a phone to find your yardage if you can't see the pin, use an anemometer to find wind speed, huge advances in biomechanical science to optimize the swing... Of course the pros can't use anemometers and range finders when playing, but they have access to so much science through their sponsors and I'm sure they utilize every bit of science, maths, and statistics in their game that they can, or at least I would if I was a pro.
Shooting is somewhat similar. Rifles started out with smooth bores, lower BC bullets, less efficient powder, no ballistics calculator solutions but only a written down dope from shooting experience. Way back in the day, shooting, even for the best, would have involved a lot more feel. Then enter today's rifles, powder, and bullets that are incredibly high quality and available to most consumers, sometimes straight from the factory. Anemometers, crazy accurate range finders, ballistics calculators, fantastic tools for measurements of loaded cartridges and their velocities.
The advances in technology of both of these sports have (or can) turn the game of feel into a science. It depends on how complicated you want to make each if these games.
In the end, I agree with a couple of the comments on the fact that the pure ability of being proficient in the game (pulling the trigger without flinch or hitting the ball where you want to) is much harder to do with golf. It still requires more feel and has, I think, more of the human element involved if a person is allowed to have every tool in existence at their disposal. The departure of the two being more similar in terms of "feel" happened a long long time ago.