Any track based tyre is going to be noiser.
Wider, softer tread blocks, less tread, etc. Physically there is so much more rubber actually contacting the road.
can't have it all!
i very much doubt the sidewalls is pushing more energy to the spring, the difference would be marginal, i suspect it's tyre on the inside of the wheel arch.
not only that but while a tyre may be advertised as 225/40/18 for example there is a big variation on actually how wide a tyre is. vredestein for example run very wide where as falken generally run on the thinner side. EG 225 may actually be 230 wide on vred where as it may only be 218 on a Falken.
combined with more squared off sidewalls rather than rounded sidewalls of road tyres you are more likely to get contact with the arch.