Well, Ol' Doodle is something of an expert on this trip having driven Mlps/St. Paul to San Diego in May of 2010 and then again this year in June for vacation. Doodle will also be driving to Los Angeles for the Rose Bowl, and then just a shade over 2 weeks later, driving to San Diego for a company meeting.
Now, in May/June (both the 2010 and 2015 vacation trips)...the mountain route (I-70) through Colorado is absolutely gorgeous and almost devoid of weather issues and is absolutely the fastest way. Doodle says "almost devoid of weather issues" because actually on that 2010 trip, up near the peak of the elevation just west of the Eisenhower Tunnel we actually did see some snow flurries. Anyway, it is the quickest and most logical way to go to SoCal from the upper Midwest. But heed the warnings of others....the roughly 100-mile stretch through Utah between Green River and Salina LITERALLY has no services. It's not a joking, "Whoa...hahaha...dude we're out in the middle of nowhere". NO. It's absolutely 100% truth. There is NOTHING out there. No services whatsoever. The few exits you will see will say something like "no services, local access only". Basically, what that means is that all of the freeway exits in that stretch are essentially some rancher's driveway. Cell service can be spotty out there as well. As you approach Green River heading west, or Salina heading east, you'll see billboards and signs warning you to fill up on gas and whatnot because you're heading out into no man's land.
Anyway, for a Dec/Jan trip, you really shouldn't even be contemplating the I-70 route through the Rockies unless you plan on bringing chains with you. Doodle knows dozens of people in Denver, Breckenridge, Vail, Colorado Springs...frankly, all over the state. And even if all of them called Doodle an hour before the Doodlemobile was scheduled to trek through their area and said the weather was absolutely ideal....the fact remains that 15 minutes after hanging up that call, there could be a full-on blizzard. It's just a reality of the Rockies and frankly, not worth the risk.
So there are really two remaining viable routes to choose from, both of which assume heading south to KC and then on to Wichita. From Wichita it's either:
US-400/54 west to Tucumcari, NM where it connects to I-40. US-400/54 is 4-lane from Wichita to about Kingman (roughly 40 miles) and then the remaining 380+ is pretty much all 2-lane to Tucumcari/I-40.
or
If the weather is bad, or if you simply cannot stomach the thought of that much driving on a 2-laner (and who could blame you for that!?), or want to avoid small town speed traps, or are worried about the uncertainty of gas/convenience store availability (esp. late at night), then stick to the major interstates and take I-35 all the way to OKC and catch I-40 there. It adds almost exactly 100 miles to the trip vs. the route above, but if you can cover those 100 miles faster or with more peace of mind, then it may be worth it overall.
Assuming normal weather/road conditions and an average speed of 60MPH on the 400-mile US 400/54 route (due to slowing for truck traffic, going through small towns, etc.) and an average of 75MPH on the 500-mile I-35/40 route, the driving time would actually be virtually identical at right around 7 hours (assuming a couple of stops).
So it really comes down to weather/road conditions and your overall comfort level with each route.
Here are several links discussing the US 54 vs. I-40 choice.
http://www.tripadvisor.com/ShowTopi...te_54_Wichita_Tumcumcari_good-Road_Trips.html
http://www.fodors.com/community/uni...rom-tucumcari-to-wichita-good-or-bad-idea.cfm
http://www.city-data.com/forum/wichita/207538-best-driving-route-phoenix-wichita.html