I'm assuming that it doesn't fold up since it's a jogging stroller. If that's the case, you won't be able to take it on the monorail or the
Disneyland Railroad. But you wouldn't be able to take the rental strollers on those anyway. Other than that, you shouldn't have any problems. The width of it definitely won't limit where you can go. We took our side-by-side double stroller to WDW and didn't have any problems at all. And because it folds up, we were able to take it on the monorail, etc. We're also taking it with us to DL next week.
The nicest thing about bringing your own is being able to keep the kids in it all the way back to your hotel and in DTD. We rented strollers last year, and they were great while we were in the parks, but that walk back to the room each night (even though we were very nearby at the GCH) carrying two sleepy little girls was pretty rough on all of us.