A bit late on the reply from the original date but I have tested a sleeve of e5’s and Q Stars. The temperature was 52 degrees, Vokey SM4 60-07 at the chipping practice area, shots taken from various points (flat, up slope, down slope, and perpendicular to slope with cup down) and distances, with three shots for each ball followed up with putting.
Both have very similar feel off the face which was very good and ball flight was similar. I will test further with Driver and iron shots to determine any difference in ball flight. The Bridgestone e5 had a slight advantage in stopping power which was more desirable on the flat and down sloping green shots. The Q Star however I gave a slight advantage to on shots taken perpendicular to the cup down slope. I say this because I could chip the ball up slope from the cup and get it to roll right up to the cup where the e5 would stop a bit shorter. Impressions: Both are great short game balls for the mid to the more aspiring handicappers (closing 100 consistently). As for determining which is better for your short game I will say that depends on how you chip, whether you like marginally extra roll, and whether the greens are flat or sloping from the angle you attack it.
As for putting both felt too similar at least at this temperature for me to deduce any major difference leading up to a preference for either. A warmer day may provide for a better analysis. The choice of either in regards to putting I think will really be predicated on the type of putter face used (forged, metal insert or composite insert) and the desired feedback.