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Not necessarily....
Dropping down to I-10 isn't necessarily going to avoid bad weather. It really depends on where the storm is, and where it's headed. My folks had to stop in western Texas on I-10 one spring, in Van Horn, because of bad weather. The problem down there? They don't have the readily-available snow moving and anti-ice equipment that I-40 and other points north have. They have to scramble.
The OP is best off using I-40. He may find some nasty construction along the way (I-40 in NM is forever being worked on!), and maybe a storm or two that will have him pulling off on a ramp. If he can travel in the earlier morning out of LA and Barstow, he may avoid at least a little of the desert heat as he crosses the Mojave Desert between Barstow and Needles.
Donna
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I should probably have mentioned two of my lifetime hobbies include maps and weather so I'm on the same page as you. OP definitely should take 40. Me? We shall see...