Have you driven either? As you say, they're not apples to apples, so after trying both you'll probably know pretty quick which you prefer. I test drove an Edge a few years ago (I don't remember if it was a 2.0T or 3.5) and found it fine. Just fine, not great. But again, there are SO many other options in this segment. I guess the Edge may win on price?
While we're throwing out random cars, and since you're torn between a Japanese sport sedan and a Domestic CUV, why not split the difference? Toyota Venza. Those are great cars.
Also, one thing to consider with the TLX (assuming you're looking at the SH-AWD version): with earlier models (up to the refresh in 2018) there was widespread criticism about the honda 9-speed transmission -- jerky shifts, etc. Not sure how bad it really was, just something to look out for.