It seems risky to judge this hotel negatively (moves your "helpful" rate on tripadvisor down :-)), but let me do it anyway, because there are serious drawbacks with this house.
This Medici palace with an axis towards the Cologne Dom is surely one of the most gorgeous hotels in the world. But to get it full and make it pay (which has not been easy and still is not), the management has to cut corners and agree to arrangements that are not helpful in preserving a *****L rating.
Many of the rooms are nice, but not the basic ones, and some singles are cramped and tiny. Public rooms are okay, ways are long. The spa area is very nice.
If you want to park your car, eat breakfast, and check your mail in the room, you'll pay more for those "extras" than for an entire room in downtown Cologne. One understands the strategy to have room specials and make money via the extras, but, really...
My main problem was the head concierge the second time I checked in in one week. I had received a nice upgrade the first time and had been told when checking out that I would receive the same when coming back. When I did, the new head concierge quite directly told me that to ask for this was greedy and showed me some rooms in the lower category. Okay, I had a good deal, but why first offer it? Denying a promised upgrade (a promise I had not asked for) is a downgrade and decidedly unfriendly. She said, however, that if I came back a third time, which I had planned, then a nicer room would be available and there would be an upgrade. I took a small single and it was okay, but decidedly not splendid (not enough space to put your luggage, not even one bag!), but when I checked out with the same lady and asked for the 3rd booking, she said that indeed plenty of rooms would be available (midweek high summer) and that I could have the upgrade... for €30! I then declined and took my business elsewhere; in this class of hotel, this level of unprofessionality is really offensive.
I should also add that the hotel hosts a lot of weddings, business functions etc. which can get extremely noisy, and as these events are what matters for the house, nobody will ever take care that people can sleep at 4.30 am.
Altogether, an okay hotel with some very mixed service (the 1st time that week I stayed there, all staff was very friendly indeed) in absolutely splendid surroundings. I think to eat there (incl. Sunday brunch) or to look around is preferable over staying there, unless one gets a high-class room at an adequate price (or doesn't care about a price-value connection).
Too bad; this could be a really good hotel; it would be tough to make that happen (because of the business model), but it seems that on the personnel level, one isn't even trying.