In the end it is all about how the stabilisers wobble when you are aiming (shot cycle), whether you are in harmony with this movement or fighting against it. If you are planning to put loads of weight on the rods then they need to be stiffer. It also depends on whether you are shooting recurve or compound.
The primary objective is to remove torque and help you settle on the Gold, a secondary benefit is vibration dampening a £90 Avalon stabiliser will do this...
If recurve remember heavy is not always best, especially when you have 10 seconds left and you have just been blown off the gold it takes a lot of effort to get back again.
Personally I shoot the Gillo GS6 (colour is a marmite moment). the stiffer GS8 & 9 just did not work for me at the target, others shooting similar draw weights and bows preferred the stiffer rods and more weight.
Compound may depend on the bow you are shooting and the torque created by the cable guard.
Otherwise just buy what you like the look of and can afford.
I remember when the Blades first came out everyone went mad for them (all those wind cheating benefits), to me they seemed a bit soft for compound but that did not seem to matter for 3 months then they bought out the ES...
My first longrod was a golf club, with the head still on a 6 iron where it could be rotated to get optimal balance - we were still learning then yet my scores improved
