Wild Turkey's nose presents a lot of leather, spicey perfume, and citrus. There is a bit of oak and char for authenticity. The nose gives up rye graininess and it is warm..........very nice.
The Rittenhouse is darker in color, is a touch more floral, is warmer, and its oak seems slightly decayed..........also a very nice nose.
Wild Turkey has excellent upfront sweetness, is rich and viscous, and warms the back of the mouth with a mild spicy sting.
Rittenhouse has a rich texture that is earthy in its sweetness. It bites with more edge, but strangely its sweetness lingers a mite longer.
I find the WT to be smoother, more sophisticated, more balanced, and slightly milder and maybe fruitier.............an excellent whiskey, especially for around $20.
I find the RH to be more robust in its deeper sweetness (what I would like to call a rye sweetness) and maybe richer, it has more of an edge, and it has more spicy bite while yet holding its molasses-like sweetness. It is also in the $20 range and is an excellent buy in whiskey in my opinion.
I would not pick a favorite of these two...........they both can fit a rye niche and both have strengths (and differences) enough to recommend them.
Have a nice day!