More likely?

[SingingAnalyst]

I can see the GOP nominating someone who is cautiously pro-choice. That is, they oppose overturning Roe or making abortion illegal, but they sill support waiting periods, parental consent, ultrasound requirements, etc., and still express a general desire to limit abortions with particularly strong condemnation of sex-selection abortions (female infanticide). I can also see the GOP platform reflecting these views, which would be considered "pro-life" by pro-life Millennials (though not by staunch pro-lifers).

Such a Republican would also put in a good word for pro-life crisis pregnancy centers. The pro-choice (pro-abortion?) activists would probably not be satisfied, but at least a major issue of theirs-- that the GOP would force women to have dangerous, back-alley abortions-- would be neutralized.

As for pro-life Democrats: I believe it is a complete lost cause. Such a Democrat would have to repudiate nearly a half century of evolution in Democratic thought, going back to McGovern. While there are still some pro-life Dems out there, there are not enough to nominate a candidate in my opinion.

[SingingAnalyst]

http://www.pewresearch.org/fact-tank/2016/04/08/on-abortion-persistent-divides-between-and-within-the-two-parties-2/

According to that link, this is how the views "roughly" break down between the parties (I paraphrased):

Republicans: 59% Pro-Life, 38% Pro-Choice
  - Conservative: 68% Pro-Life, 30% Pro-Choice
  - Moderate/Liberal: 54% Pro-Life, 41% Pro-Life

Democrats: 70% Pro-Choice, 28% Pro-Life
  - Liberal: 84% Pro-Choice, 14% Pro-Life
  - Moderate/Conservative: 60% Pro-Choice, 38% Pro-Life

Those numbers seem a bit high for "Pro-Choice," but it still would give the impression there are significantly more pro-choice Republicans than pro-life Democrats, so I'll go with that one.

EDIT: I'd also GUESS (no idea) that most pro-choice Republicans are younger and most pro-life Democrats are older, so that's another reason to believe the pro-choice Repub is more likely.

Besides Joe Manchin, are any pro-life Dems prominent in public life?

Ted Kennedy, Jesse Jackson, Al Gore, and Dick Gephardt were all once pro-life, and changed. So the Dem momentum is clearly in the pro-choice direction.

For the Dems to nominate a pro-lifer is about as likely as them nominating one who opposed the Civil Rights Act of 1964 (which 21 Democratic Senators voted against).