Guys, guys, guys .... the external balance damper needs a certain amount of what is called 'moment'. Moment is determined by:
1. taking the exact distance from the center of the weight to the center of the crank snout
2. the exact amount of the weight
3. multiply the 2 together to get a moment, typically specified in in-oz
So a 10 oz weight at 2" from the crank center will have the same moment as 5 oz at 4". Both will be 20 in-oz of moment and both will provide the same external imbalance to the engine.
Sorry to say this but post #9 is not correct. There is no set relationship between the amount of the damper's weight and the weight of imbalance; the 2 numbers are totally independent of each other. The damper without the weight can weigh 1 oz or 100 lbs; regardless of the damper's overall weight, the same imbalance weight attached to either one at the same distance from crank center will create the exact same moment.
The moment also has to be at a certain angle to the crank key. OP, what bothers me with the pix you show is that the angles between the crank keyways and the center of the weights is quite different between the 2. That is a problem. However, the top pix shows a small recess machined inside the hub that extends under the bolt-on weight. As best I can tell, that effectively makes the angle difference a tad worse but we can't really see it. BUT it may well be that the 2nd pix is a stock photo, and does not really represent the 360 damper; I am guessing that is what is going on.
So if you get the new 360 damper, compare the angle between the keyway and the center of the weight to the old one to see if they are pretty close.
For me, if the old damper is pretty good, then I'd put on a timing tape as suggested.