Due to some odd arrival dates, we ended up staying in both Le Duplex and La Veranda at the La Terrasse des Climats units and we loved both of them. As a side note, since they share a spectacular deck (with a removable partition) this would be perfect to split with a group of three couples. Both units give you the best of both worlds, where you are in a very modern apartment, with all the bells, whistles and outlets, but the views offer fantastic views of the old city, as well as views of vineyards and the cathedral from the bedrooms. Being directly off the Place Carnot makes walking all over the city extremely easy and convenient.
The Duplex has a cozier feel, with the bedroom on the second floor and the living space below. "Cozy" isn't code for small, because there is a lot of living space and is big for two people and I think it would be manageable if you wanted to squeeze in four. The only odd thing is that the water closet is on the bottom floor and the bathroom is on the top, so you may need to make some middle of the night trips down the stairs. Also, to enter, you take an elevator and then a flight of stairs to the apartment. The stairwell traps a ton of heat and you will have a small moment of freaking out when you first get there if you arrive on a hot summer day. Fear not, the rest of the unit is as comfortable as can be.
The Veranda unit is very big for four people and was downright palatial for two of us. The entrance is a private elevator, which is both cool and convenient. The main living space has a series of sliding doors which open the whole space to the deck, which is pretty spectacular.
Both places have very well appointed and very comfortable bedrooms, big and modern bathrooms and great kitchens. The decks might be even better than they appear in the pictures. The AC was an unexpected pleasure and, in general, both of these apartments provide a ton of modern conveniences that you might not think would be available considering the location and the age of the city. The remodel of this space was so smartly done, I really couldn't think of many ways to improve on anything. When we return to Beaune these will be our first and second choices for places to stay.