I currently drive a 2011 Genesis with the 4.6 (Based on the same Tau platform as the 5.0 in the Equus) and it has been rock solid. One minor accident in the rear left side before I bought it at 68k miles in February and I am just about to break 78k (Or I might've this weekend) No major issues, some mildly expensive 'upkeep' things like a transmission flush but that was every 60k miles so it happened before I bought it. I do have the ZF 6 speed auto whereas the later model Genesis and Equus use a Hyundai 8 speed auto. I haven't heard anything bad about them, but I'm sure they're not up to the ZF quality.
Overall maintenance 'would' be cheaper on the Equus than an Audi/Mercedes except how limited they are. Most everything on my Genesis is more Kia priced than Audi priced.
Considering I own one of them I'm biased, but I'd say any one of these is good. Kia K900 (It's on the same RWD Genesis platform, you might not like cadenza-like front though), a 2nd generation Genesis (2015+), or a low-mileage E class, or the Equus.
The Equus really is incredible, and is probably second only to the 2nd generation Genesis IMO. The new Genesis very nearly outdid the 2014 E class I looked at and was way beyond the previous generation E class (2011). All these cars are incredible though, only one I've never driven is the k900 and it is basically a Genesis so it shouldn't be bad