Is there a word which means one who prefers older ways?

Solution 1:

Mill-horse

And what a couple of old patriarchs shall we become, going in the mill-horse round; getting sons and daughters; providing nurses for them first, governors and governesses next; teaching them lessons their fathers never practised, nor which their mother, as her parents will say, was much the better for!
Clarissa Harlowe

Roland is a great personage, an honest nobody, a mill-horse at the wheel of office. Blackwood's Edinburgh Magazine - Volume 55, No. 343, May 1844

But I had achieved a frigate and a Princess, and that was not so bad for a beginning, and more than enough to show off with before those dull unadventurous folk who continued on their mill-horse round at home.
Dream Days

All examples lifted from Wordnik - https://www.wordnik.com/words/mill-horse

Solution 2:

I think you could use traditionalist for both your examples. From Oxford Dictionaries:

NOUN
An advocate of maintaining tradition, especially so as to resist change.

ADJECTIVE
Advocating the upholding or maintenance of tradition.

Even where the new lanes have been added, traffic permitting, John prefers to make lane changes to conform with where the older lanes used to take him; he's rather traditional(ist) in that behavior.

Mary is quite the traditionalist, preferring to use a manual pencil sharpener to an electric one.

Your first example seems rather extreme (what if a fast-moving vehicle comes up behind John while he's straddling the new lanes?), so you might prefer a stronger adjective there, like hidebound: