I've had two models of Scotty and the KM350.
First, just to note, below is my subjective experience.
In comparison to some of the regular putters I've tried, Scotty is in another league, much better quality of construction and feel.
But after getting used to the KM350, it's a shock to the system to go back to Scotty. The feel are worlds apart, putting the KM350 in yet another league.
The head of the Scotty is much larger yet lighter. Requires a stronger stroke to feel the head.
The smaller but heavier KM350 will swing with the lightest of touch, giving me much better feel. I am aware of the head at all times.
Feel wise, Scotty is soft compared to most, but KM350 is noticeably softer still.
Because of the denser head, putts from the KM350 hold their lines well. That includes powering through from the fringe without getting as easily distorted by impact as lighter heads.
The much smaller head does take some getting used to initially. Now I find regular putting heads redundantly large. It's all relative perspective.
I've been told when playing on fast greens, a heavier head is better and vice versa. When I played on fast greens, the KM350 yielded much better result and I've not looked back since.
But note, the KM350 both requires and encourages a pure stroke. It's not as forgiving as Scotty. One may view this as positive or negative, depending on what one is after.
And of course, price wise, the Scotty is a lot friendlier to the wallet.