I think hitting them both in one weekend depends on how much time you have, as well as the weather. We drove from the Bay Area Saturday morning, and started the trail at 11:00am. By the time we reached the pass at about 6pm it was obvious we would not make Matterhorn that day. (Our original plan was to hit Matterhorn Saturday evening, then Whorl Sunday morning, then hike out in the afternoon.)
The thunderstorms slowed us down, as did our inexperience crossing the snowfields, which were firm and sun-cupped. I would like to have had an ice ax or at least some trekking poles for peace of mind.
I'm still working on the pictures.
EDIT - My profile pick is the view up towards Horse Creek Pass on Sat. July 30th, somewhere around 3pm.