1

First, xMonument Valley, Grand Canyon and xHoover Dam are not in xCalifornia.

These are two, very different trips. Either will be great in winter.
Though I'd choose Zion and Bryce over MV. Less backtracking involved, and well, Bryce in winter.

The main questions:
How are you at driving in winter conditions?
Are you allowed to use snow chains on your rental car?

xYosemite and Tahoe are more likely to require positive answers to those questions.

A third option, of course, is to simply drive up the coast to SF. "Winter conditions" there will mean rain.

2

Are you arriving and departing from San Diego or can you depart out of San Francisco (or Las Vegas?)

You will put 1600 miles (2576 Km) on your car driving option #1. That's two days on the road at least.
Driving from San Diego to San Francisco, Lake tahoe, Yosemite and back to San Diego is 200 miles shorter but a longer drive time if you take CA-1. You'r going to spend three days on the road with that option.

You can expect to pay more if you drop off the rental car somewhere other than where you rent it. There are exceptions, but until you have the contract in your hand, don't count on it.

You may encounter snow on either route.

we're worried that the trip being in winter makes a lot of difference to places like the grand canyon

That is a subjective judgement. I'd take option number one. Your mileage may vary. The Grand Canyon under snow at the higher elevations is beautiful. So are Bryce and Zion. You have to be comfortable driving on the stuff and a delay because of snow can't cause you a catastrophe with your airline reservations. Flying home from Las Vegas or San Francisco would reduce the total amount of driving and maybe provide a free day if you are delayed.

3

Assuming good weather, either would be a wonderful trip. And, they are different enough places to not be easily compared "objectively".

All sorts of good advice above.

The one scenic disadvantage of Yosemite in the winter is that the waterfalls will be low, even dry in some cases.

The relative disadvantage is that bad weather is somewhat more likely at Yosemite (average January precip 6.70", snowfall 16.1") than at Grand Canyon (average January precip 1.78", snowfall 10.4"), and the snow at Yosemite is likely to be less powdery and therefore a bit more problematic to drive on.

Grand Canyon (as well as Bryce - especially - and Zion) are, if anything, enhanced by the presence of a little snow.

For such reasons, I would prefer Grand Canyon. I would add Bryce Canyon and Zion Canyon in preference to Monument Valley. But, weather permitting, you can't go wrong with Yosemite either.

Edited by: fdbaz for clarity

4

Hi,
i've actually been to both in January(to Yosemite multiple times in December/January) and i would choose Yosemite over Grand Canyon any day. there is so much to see and do in Yosemite: waterfalls, sequoias, lots of hikes, you can drive up to Badger pass for skiing/snowshoeing.
from San Diego you can rent a car and in 8 hours you're near Yosemite. we usually stay in Mariposa(it's a small town about 45 minutes from the main entrance): pretty cheap accomodations (Mariposa Inn), good coffee, cute downtown and the drive into the park is just beautiful following the Merced river. or you can stay in Oakhurst; it's a bigger town with less character but more accomodations/fast food chains, etc. and you'll be pretty close to Mariposa Grove with giant sequoias.
weather wise, last January there was no snow in Yosemite when we were there, it was still pretty cold, 40s-50sF so dress in layers and bring warm clothes. usually though, there is snow in the valley and up in the mountains and Tioga Pass road/Glacier point is closed, but you can still drive to Mariposa Grove/Badger Pass(unless there is a snowstorm). if there is snow, you'll have to use chains on your car, but the roads in the valley are always cleared.
waterfalls are really nice as well in winter especially the Bridalveil fall and the yosemite falls. and there are very few people compared to spring/summer months.
Grand Canyon in winter is beautiful but there is definitely snow there as well and it is COLD. but to get there you drive through the Californian and then Arizonan desert so there is no snow there and the weather is sunny and quite warm(not at night though).
well, hopefully this was helpful. have fun wherever you decide to go!