I don't think it makes too much difference which come first. The two things have to fit together.
There is only a certain set of notes that will really fit in any given chord. Of course you can use any note as a passing tone. Many times you have no control about it in the first place.

For me it is less work to have the chord progression first. Having the chord progression puts some fences around the possible melody. Sometimes a melody just gets there first so you have to deal with it.

It also depends on how things come about. Working alone is one condition, working with a group of people is another. Sorting all that out before one goes into a costly studio is a very good idea...lol

Nothing is easy, but not having to deal with a vocalist certainly reduces the work load. Lyrics are a whole nother kettle of fish...lol I guess we all wish we were highly skilled singer/songwriters.

Billy

“Amazing! I’ll be working with Jaco Pastorius, Charlie Parker, Art Tatum, and Buddy Rich, and you’re telling me it’s not that great of a gig?
“Well…” Saint Peter, hesitated, “God’s got this girlfriend who thinks she can sing…”