There are several factors that will contribute to the more "sluggish" responsiveness of the Tiguan, despite the fact that the two engines generate about the same torque at about the same engine speed (236 lb.ft @ 1750 RPM vs. 221 @ 1600). As you have correctly pointed out, vehicle mass is one of the most significant ones, and the Tiguan is at a disadvantage here as it is about 500 lbs heavier. The torque curve is the second factor. In case of the CJAA engine, the peak torque remains flat between 1750 and 2500 RPM. I do not know what the torque curve looks like for the Tiguan's gasser, but if it drops off above 1600 RPM, that will also negatively impact the car's responsiveness. Third, the gearing of the transmission and the transmission type will have some impact on how responsive the vehicle is. With manual transmission, the driver decides the shift points. Automatic tranny doesn't give you that freedom, it decides when to shift. And, there are other factors, such as rolling resistance and drag coefficient, both of which put heavier, taller vehicles at an additional disadvantage. When you think about all this, the only fair comparison of these two power plants would be to yank the diesel off the GSW and drop in the Tiguan's gasser. That would eliminate all of the above mentioned factors, and you would really be comparing diesel with gasser.
As for the oil dilution issue - Mazda originally designed the engine with a compression ratio of 13.5 : 1, which was low enough to keep the NOx content in the exhaust gasses below the T2B5 limit, which eliminated the need for injecting urea, simplifying the emissions system significantly. Nitrous oxides are formed when both of the elements are exposed to high temperature and high pressure. The higher these two parameters are raised, the more likely it is that NOx will form. For that reason, NOx are usually not a significant concern in gas engines as their compression ratios and associated combustion temperatures simply aren't high enough to produce them in quantities that would necessitate aftertreatment. That was the reason why Mazda dropped the compression ratio of their new diesel so low. By doing so, they achieved their goal of reducing the NOx emissions below the T2B5 threshold, but they didn't expect that the unburnt fuel would condense on the cylinder walls in such quantities that it would dilute the engine oil. What surprises me is that Mazda supposedly fixed the whole issue by increasing the compression ratio from 13.5 : 1 to mere 14.4 : 1. It would seem that increasing the compression ratio by such a small increment would not have significant impact on the issue at hand. Every other modern on-road diesel engine I know of has a compression ratio around 17.5 : 1. This, of course, necessitates urea injection, but so does Mazda's 14.4 : 1 ratio. So, why not increase the ratio all the way to what everybody else is doing (17.5 : 1) and be done with the whole mess?