I haven't stayed in either in the last year, but I use to travel to Stockholm 4-5 times/year and have stayed at both hotels many times. The Hilton was a SAS/Radisson back then. The Hilton rooms have a more modern feel to them, I remember the heated towel racks and heated floors in the bathrooms. The TV was a bit limited then, but Hilton may have upgraded it.

Both hotels are well located, roughly opposite ends of Stockholms old town, lots of restaurants and tourist shopping. The Sheraton is much closer to the Central station which is the center of Public transport. It is a bit closer to the big department stores, and a major walking street with restaurants and shopping.

When I am in Stockholm with customers we use the Sheraton, because of the slightly better location, but if the $ matter the Hilton is a good second choice.