Driving in the winter (Dec-Jan) from Ohio to California

Both I-80 and I-70 being major highways are kept plowed during the winter months. Assuming you are not driving during a snow storm, both should be similar in terms of driving difficulty. I would suggest watching the weather and then make your decision right before you leave based on what is coming in. If there are no fronts approaching, enjoy I-80, if there are storms try to estimate which route will have less new or falling snow.

Yes it would be advisable to have chains, as they can be required by law on some stretches of highway and are useful in a variety of winter conditions. But don't just buy a pair and throw them in your trunk, head out to a dirt road and practice putting them on and adjusting them a few times before your trip.

And no matter what tires, chains or studs you are using, remember speed kills. You can not maintain full highway speeds during the winter months in snow country, you need to slow down when driving on snow. Can't begin to count the number of idiots who would speed by me on the highways when I lived in Wyoming, only to be seen a short while later standing by the roadside with their car off in a snow bank.

You are probably likely to encounter somewhat less snow on I-80 due to its lower elevation. However, there is a significant chance of snow along either route. Note that I-80 also crosses snowy mountains in Utah and in eastern California. Furthermore, if you are crossing Colorado on I-70 in November, you may well encounter snow at that time also.

In short, it would be a very good idea to be prepared for driving in snow. Several of those states have laws requiring you to use tire chains when conditions demand it. (Signs will tell you when this is the case; usually you are not allowed to use chains otherwise.) Winter tires (marked M+S) help but under some conditions may not be sufficient to satisfy the law, unless you also have four-wheel drive. If you are not appropriately equipped, you may have to suspend your trip to wait out the weather.

Carrying blankets, warm clothes, snow boots, extra food, etc, would also be wise.

I would be afraid to travel either. I traveled I-80 in late September last year, and through fog, rain, hail, sleet and snow, I was afraid for our lives several times! I-80 through the Midwest is great. But there are long steep inclines and declines through Wyoming, and I could barely keep on the road when there was slush or snow on it. If it were me, I would drive south, and take I-60 or even a more southern highway.