Rose wines have a higher level of tannins, which cause a dry, puckery

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Rose wines have a higher level of tannins, which cause a dry, puckery sensation in the mouth and throat, than white wines, but less compared to red wines.

The sentence is complicated by a non-essential modifier, which is offset between commas. Conveniently, this non-essential modifier does not change, so it can be ignored.

a) Rose wines have a higher level of tannins...than white wines, but less compared to red wines.
The structure should follow: G has a higher level of H than J, but less than K.
G has a higher level of H than J, but less compared to K

b) Rose wines have a higher level of tannins...compared to white wines, but less than red wines.
As above, with the compared to and less than switching

c) A higher level of tannins...is found more in rose wines as compared to white wines, but less compared to red wines.
A higher level of H is found in G as compared to J, but less compared to K
H and G are swapped from the examples above. Using as compared to...but less compared to is wordy, but at least it doesn't mix than/compared to like A and B
Not a fan of higher + more. more means the frequency is greater (so it's no longer an explicit rule that A>B>C), so there is a slight meaning change. Still, C is better A and B

d) A higher level of tannins...is found in rose wines as compared to white wines, but less than in red wines.
Back to the mix of compared to/less than

e) The level of tannins...found in rose wines is higher than that in white wines, but less than that in red wines.
The level found in X is higher than that in Y, but less than that in Z
This sentence no longer begins with the comparative higher, and this forces the use of that to maintain comparison across all the parts.
higher than and less than are parallel, and are much clearer than using compared to

E