This varies significantly from hotel to hotel, even though they may all share the same brand name, each hotel has its own management and business style. Also keep in mind that not all Hilton hotels are owned or operated by Hilton corporate, most are actually franchised to independent owners and management companies.
In general, Hilton corporate standards requires all Hilton Hotels to have professional uniforms for front-line staff like Front Desk where you will probably see staff dressed in more professional business attire, especially supervisors and managers. However, how the back office staff dresses probably depends on the management, staff who have little or no interaction with guests probably dress more casually, but again this depends on management.
I know Hampton Inn which is a Hilton brand, is known for having a casual workplace, they have a new line of uniforms for all departments that allow staff to choose from a selection of clothing ranging from casual to business.
I have worked for several Hilton brand hotels including Hilton Garden Inn and Hampton Inn and found most of the staff and management to be very friendly. However they have all been franchised hotels so I am not sure what its like to work at a Hilton corporate owned and managed hotel.