A CTS is RWD (or AWD) and is built on the Sigma platform An Impala is FWD and built on the Zeta platform. They are not the same car at all. As far as I know there are no other cars in the GM lineup using the current Sigma II platform except for the CTS, and only the SRX shared the previous-gen CTS’s Sigma platform.
ETA: I would add the Mercedes E550 to the list. At the price point, though, you could probably get a nice used AMG E63. 
Why buy a luxury auto if it’s a Hyundai? I think consciously or subconsciously, people like brands like BMW and Lexus because they’re thought of as premium brands. Not Hyundai. Resale value would also likely be less for a Hyundai.
It also depends on what features you’re looking for. Leather seats are easy to come by, so are fast-ish cars. A V6 Camary performs surprisingly well, 0-60 in 5.8 seconds.
W-platform.
No one buys cars like these, out of all those the BMW will probably be the cheapest to lease, as BMW is well know for subventing their leases rather generously.
I’m at an income level where I could buy a luxury vehicle at a stretch, but probably won’t ( my mortgage constrains purchases just a tad ). I’m a lot more likely to spend in the $25-35k range at most and I prefer roomier sedans. So if I were to splurge, value would inform my choices as much as performance, luxuriousness and appearances.
Accordingly I’d pretty much always go Japanese first for reliability reasons alone. I’d take the Infiniti over the Lexus both for cost reasons ( the Lexus would be over any threshhold for me ) and because traditionally the Toyota/Lexus brand has tended to isolate more from the road. Some prefer that in a luxury car, but I’d rather something just slightly sportier/more responsive.
The BMW would come next as the performance leader, but German reliability ( but sadly not repair expense ) really seems to have slumped recently.
Hyundai last, even though it is the cheapest. I’d rather a flagship standard sedan with luxury features, than an overpriced, low-end luxury car.
Looks like the 5 series sales have been struggling…same with the E class. But Hyundai has sold almost 1300 Genesis in the first month…not too bad for its class.