Spent a week in Santiago last year, shared between the Singular and Ritz Carlton. Atmosphere wise, the Ritz Carlton feels like yet another business hotel, nothing special, with the exception of select evenings with live music in the lobby. The Singular has a much more distinct vibe, which is akin to a gentleman's club, with dark tones and dark leather aplenty (although there was an oddly large number of Russian tourists on group tours crowding the lobby when I was there, ymmv). If the gym is important to you, do note that the Singular's gym is in a room with bare walls and no natural light. I wouldn't go so far as to call it dank, but the Ritz Carlton's gym is housed under a beautiful glass arcade in comparison.

F&B is stronger at the Singular than at the Ritz Carlton, if you intend on eating at the hotel. They do a great chupa de centolla. No surprise, given that their Patagonia hotel has the best restaurant within a 15min drive of Puerto Natales. However, management wasn't a notable presence at their Santiago property (unlike in Singular Patagonia where the GM came for chats during dinner). Of course, management was non-existent at the Ritz Carlton too, haha. Again, just another nice business hotel.

While the neighbourhood around the Singular is far more hip (more interesting F&B options and shops), it was also rather grimy. The protests over the last few years have taken its toll, and graffiti is everywhere. The Ritz Carlton on the other hand is situated in a more manicured but lifeless neighbourhood. Graffiti has been scrubbed, and streets are clean. Wide, walkable avenues with chain restaurants and boring banks are the vibe there.
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Overall, I'd say that Santiago isn't really much of a luxury hotel destination, or even much of a destination at all, the hotels are dependable but unexciting. Patagonia and the Los Lagos region, or anywhere else in the country really, has plenty more inspiring hotels worthy of the luxury label.