I am quite familiar with both properties. Not exactly sure what the difference is you're looking to discover, but here are my thoughts as a comparison between them.

Hilton Garden Inn is centrally located near the business district, an easy walk to the mall, stores, Etc. Express bus to downtown Seattle leaves from the public library one block away. The building features a center courtyard, with upgraded rooms being ones facing the inside, or the larger corner rooms. As a diamond, you stand a good chance of being upgraded, though you may have to ask at check-in. Standard HGI breakfast situation, although they do not bring your food to your table, so standing around waiting near the grill can be hectic if they're busy that day.

As noted, the Hilton is a bit dated, although they have refurbished some of the executive level rooms. There are a couple of Hilton Honors floors where they would likely put a diamond member, with one of them hosting the executive lounge, really just a section of the hallway in front of the elevators where they provide an evening reception and morning breakfast. They do not advertise the fact, but diamonds have the option of breakfast at the restaurant free as well; you need to give you a room number to the server beforehand. That option features cook to order eggs, as well as the food brought to you at your table. Walking into Bellevue is not a particularly attractive option, as in addition to the distance the city center is seriously up hill. They run a local area shuttle I believe every 30 minutes? To go to downtown Seattle that way, you would have them drop you off at the transit center. They do upgrade diamonds to the Hilton Honors floors, although you may have to gently bring up the fact at check-in.

I confess I don't know much about gym facilities or parking. For 50K, I'd go with the Hilton if you have a car, and the HGI if you don't as my best advice.