I'm just starting in the fall too for a CS PhD. I talked to some of the current grad students when I visited and heard there wasn't a huge difference between Weyburn and Hilgard. There seemed to be a more active social scene at Weyburn, if that's your thing, but that could also have been some sample bias.
Another thing to think about is location. Hilgard is a bit closer to campus. It's also slightly closer to TJ's, Ralph's, and Target. Weyburn is closer to KREC the graduate student gym.
Then, note that Hilgard is all studios. Weyburn has some studios, but is mostly 2 people per apartment. Studios are more expensive, and for some reason Hilgard studios are more expensive than Weyburn studios (by about $90/mo).
The last difference I can think of is parking. I remember reading somewhere on the housing site that Hilgard had fewer parking spaces and so there's usually a waitlist. Parking seems really shitty at either place though, or at any place near campus, for that matter. Weyburn apparently has tandem parking spots which sounds absolutely terrible, but for all I know Hilgard does too.
Sorry if you already knew all this stuff. Most of it is on the housing pages but it's spread out and sometimes hidden. It might be good to have the information compiled here for posterity. If anyone else knows anything else, especially if they've lived in either place, bumping metallocene2015's request for info.