How does the adjective 'obsolete' differ from other similar words?
Some common synonyms of obsolete are ancient, antiquated, antique, archaic, old, and venerable. While all these words mean "having come into existence or use in the more or less distant past," obsolete may apply to something regarded as no longer acceptable or useful even though it is still in existence.
// a computer that makes earlier models obsolete
When is 'archaic' a more appropriate choice than 'obsolete'?
In some situations, the words archaic and obsolete are roughly equivalent. However, archaic implies having the character or characteristics of a much earlier time.
// the play used archaic language to convey a sense of period
When could 'ancient' be used to replace 'obsolete'?
The synonyms ancient and obsolete are sometimes interchangeable, but ancient applies to occurrence, existence, or use in or survival from the distant past.
// ancient accounts of dragons
Interestingly, you automatically used a word in your question that you didn't even comment on—perhaps without realizing what you'd done: displace:
1 a : to remove from the usual or proper place
specifically : to expel or force to flee from home or homeland
// displaced persons
1 b : to remove from an office, status, or job
1 c obsolete : to drive out : BANISH
2 a : to move physically out of position
// a floating object displaces water
2 b : to take the place of (as in a chemical reaction) : SUPPLANT
So, in your example sentence:
The automobile displaced the horse and buggy.
I don't know if this is exactly what you're looking for, but the verb supersede is close.
From Cambridge Dictionary:
supersede — to replace something older, less effective, or less important or official:
Wireless broadband could supersede satellite radio one day.
From Merriam-Webster
1a : to cause to be set aside
1b : to force out of use as inferior.