I recently completed three nights each at these properties, which are both very nice. In a city with generally mediocre service, these two hotels stand out for being the best (better, indeed, than my limited experience at the Four Seasons and Grand Hyatt). Some observations:

-- Sheraton: I was upgraded, as a Platinum, to a beautiful two-room suite with very elegant design, gorgeous bathrooms (2), and huge balcony. The lounge is among the best in Amman, with pretty comprehensive breakfast and typical evening snacks and alcohol. The service was very friendly and responsive, including dedicated check-in for Platinum/club guests off of the lobby. Location, on the Fifth Circle, is central, but not within immediate walking distance of much.

-- Le Meridien: Also given a two-room suite, not as nice as Sheraton, but very comfortable. Again the service was very responsive -- every time I called for assistance, they were amazingly prompt. The structure is not as impressive as the Sheraton (LeM must be older), but the lobby is more elegant. The lounge is a step below the Sheraton in terms of size and amenities, but has free computer/internet, which the Sheraton does not if I recall correctly. Restaurants are, on balance, the best in any hotel in Amman, with Chinese (at which I ate -- food was so-so, as expected, but service was outstanding), Benihana (I know, not what you'd want if you were visiting Amman), and excellent-looking Arabic and Steak restaurants, plus a lobby bar and Italian restaurant. Breakfast is also probably the best (better than Four Seasons and Hyatt, comparable to InterContinental) of the typical Arabic/international buffets that all hotels offer. There's also full-service Starbucks outlet connected to the lobby. Location is Shmeisani, within walking distance to a neighborhood with fun local restaurants and nightlife venues. One strange aspect is that there are no personal items (e.g., toiletries) available at the gift shop -- you have to leave the hotel for this, although right outside across the street there are a few shops. I found the "hotel taxis" outside to be especially good -- they charge the usual premium, but are clean and with English-speaking drivers.

I have now stayed at most five-star hotels in Amman, and I would assign the following rankings, taking into account physical space, location, service, and restaurants:

Top tier:
Le Royal (haven't stayed)
Le Meridien
Sheraton
Four Seasons
Grand Hyatt

Mid tier:
Intercontinental
Kempinski (haven't stayed)

Bottom tier:
Marriott
Crowne Plaza