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.