As long as we play in the same fields in online tourneys, i think this discussion has it's place
But it would be better if we leave emotions or feelings out of the equation as much as possible .... we just look at stats (as Mike stated). If we do that, some answers are quite obvious.
Long game:
Mouse swingers generally hit more fairways and greens. Being a mouse swinger myself, i can say, that it isn't a walk in the park on tour pro to do this. I would say that my driving stats should be a little bit worse, compared to real PGA Tour pros. I'm hitting around 80 %. That's a bit much, but we played a lot of courses so far with rather generous fairways.
GIR i hover mostly between 65 and 70 % - that's well inline with the pros. 3-clickers often cannot match these numbers.
Conclusion: The best mouse swingers hit 5 - 10% more fairways than the best clickers (makes only sense to compare the best players of the different swing mechanics). And they hit 5 % more GIR - although we had 3-clickers leading in this statistic as well. There isn't that much of a difference, but you can argue that the long game is a little bit tougher 3-clicking. In the big picture (comparings the stats to real pros) the 3-clicking stats are more in line than the mouse swing stats. So you maybe toughen up the penalty for mouse swingers (only a tad and especially for the driver). I think, the GIR stats are right on the money.
Short game:
There is no significant difference between the two swing mechanic to be found here. Clickers and swingers are equally good. The one thing important to read out of the stats is, that scrambling and especially sand play is way, way to easy in the game. The averages of the top players are 15% better at scrambling and over 20 % better at sand saves than the best Tour pros can manage. So, this part of the game has to toughen up for both swing mechanics to get realistic scoring.
Putting: No difference as well. The best putters are putting 0.25 putts/GIR better than Jordan Spieth ..... this is a lot! Averages of 24-25 putts per round are quite common. 4-5 strokes better as they should be.
Comparing the complexity/difficulty of the two swing mechanics:
Physically it is easier to click. You don't have to move your hand to execute the shot. When mouse swinging a lot can go wrong because you can move your hand in the wrong angle, on the wrong path and too slow or too fast. So the potential of massive error is higher.
Swing meter: The swing meter in Perfect Golf is rather slow 3-clicking (compared to former Golf games). So the danger of clicking way to early or way too late is rather small. The rather slow speed of the meter doesn't force rhythm to be involved - it's more a question of hand/eye coordination. You don't have to "feel" when the right moment to click for the snap is (like it is in Links on the highest difficulty level). Your eye can see it, send the "message" to your finger, and then click. That is the reason, why the penalty for missing the snap slightly in some sort has to be harsh on tour pro - because it is really uncommon to completely mistime the snap.
This all only is an issue on Tour pro. The last tournament on Pro - Richiebro won with a score of -44. I had no business shooting that low. So you could argue that mouse swingers are at disadvantage on anythin under tour pro.
I would like the devs to tinker with the penalty for mistimings/missed snaps in the coming updates. Penalize the mouse swingers a tad more on drivers for a missed timing .... see how the stats change. Speed up the swing meter for three clickers, but reduce the penalty for the snap ... see how the stats change. But first of all: Make the scrambling and the putting harder. But not by making the swing mechanic more difficult for these shots (chipping straight or putting relatively straight isn't that difficult in real life), but by changing the physics for these shots. All of the shots around the green have way too much bite after impact with the ground. Don't bring the stats in line with the wrong tools.