I can't fully argue for this, but my gut says that Turing and all he represents is ultimately valorized by AI-stuff, but Church is the opposite. The former started from the point of view of purity, minimum possible conditions/possibilities, and abstraction/"pure" computation; the latter cared about ways we could actually think, and cared not for implementation, but articulation and the furthering of abstraction.
One point of view for this is that Turing built practical computers during the war effort and then was forbidden by his own government to continue to build computers so had to retreat to theory. Church had no practical experience with computers and was looking as much to expand the theory of Mathematics itself. In their collaborations together and communications across an ocean they married a lot of the practical and the theory and solidified core parts of the theory (imperative/functional dualism [the Church-Turing Theorem often shortened to the Turing Theorem ignoring the contributions of both]; the Halting Problem [and its relationship to Church's Theorem]; more).
I think it's wrong to see it as a competition, because their collaboration did so much together. Computer Science has "two dads" and that feels appropriate for several reasons, including how Turing died. It is somewhat important to Computer Science that Church and Turing met in the middle, one with the deep raw mathematical theory background and the other with the practical (but at the time unacknowledged) background.
Also, it would be somewhat remiss to ignore that Turing did care about implementation and wanted to get back to practical implementation but wasn't allowed. There's a deep tragedy there and lot of questions about what would have been different if things hadn't been classified in the same way by the UK government. Though also in that case perhaps it would have cost us the Church collaboration that helped firm up the theory so well in our timeline.
This is a strong point, "the latter cared about ways we could actually think, and cared not for implementation, but articulation and the furthering of abstraction." I will look into this more. Thank you
