I've been meaning to offer some diagrams to illustrate sailing characteristics, as it's an intriguing subject that fascinates me. Finally got around to thumbing through 700+ pages of the "Bible"* to find a pic. This post specifically addresses: is an Island 'better' or 'worse' on one tack or another whilst reefed.

This illustration (p337) is actually comparing different mast sections/sail leading edge position, examining the L/D ratio (Lift versus Drag) using a wind tunnel. However, when the Island sail is furled partially (and
only then), it presents a profile very similar to (A) when on a port tack, and (C) when on a starboard tack (although you need to mentally flip that pic to relate it to the AI/TI).
In both cases, ignore the mast profile, and substitute the round profile of the AI/TI furled mast, as it's not much different in terms of airflow.
The results:
A : L/D = 6.7
B : L/D = 8.0
C : L/D = 9.9
From this we can see that C (our starboard tack) is some
40% improvement over A (port tack). This is because profile C has the least 'reversed flow vortex' on the low-pressure (leeward) side of the sail, and it is this side that creates the lift that drives the boat.
So, for a
furled sail, without changing the degree of reefing, we should expect the AI/TI to perform better on a starboard tack.
There is much more to this subject of course... as time permits, I'll try to illustrate some other very significant factors.
Incidentally, an unfurled sleeved AI/TI sail is actually very efficient in terms of mast turbulence; my guess is that it would be midway between B and C on
either tack!
* CA Marchaj
Aero-Hydrodynamics of Sailing