Pheonicia would be similar to the Shelbourne (slightly less upmarket though but best local comparison I can think of) - grand old hotel that has been recently renovated but perhaps limited in space for amenities. I've been in it but didn't stay there. It's right outside the main gate into the pedestrian old city, so great location. There is a huge bus terminal outside, so very busy, maybe look for a room at the back?
The excelsior is a modern hotel on the seafront, more resort type amenties but less atmosphere. A few minutes further from the old town. It depends what you're looking for really but i'd go for the Pheonicia personally!
If you're driving (and cars are very cheap - we paid about €80 for a week in March), you can get anywhere in an hour (27kms end to end), it's really not very big so it does work well to stay anywhere on the island and commute. I stayed on Gozo and had no trouble or delays going over and back on the ferry for sightseeing.
Do make sure that you book tickets in advance if you're interested in the archeological sites.