Morgan Freeman vs Woody Harrelson.

No real parameters here. Just which one do you think is a bigger star and maybe a short statement why.

Personally, I lean Woody. I think Cheers puts him over the top. Morgan doesn't really have any thing like that on his resume.

Woody Harrelson does such a great job of picking scripts, that gets a lot of points. Completely offbeat stuff like his role in Edge of Seventeen, or Semi Pro and he's great in them, with the occasional blockbuster like Hunger games.
But MF has bigger roles in bigger movies overall.

So Morgan wins.

If I had to erase all the movies with one of them in it, I'd erase Woody's movies. I'd miss the Zombielands terribly, but The Dark Knight was so good. It's almost not fair considering Freeman wasn't the main star.

Agasaurus Tex said:

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....and Morgan was in Shawshank.

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I've never been as big of a fan of Shawshank as most of the movie guys around here. However, as I've gotten older and seen guys get out of corporate America after decades, that movie has a much deeper meaning.

Lets also not sleep on Freeman's time in The Electric Company. I feel like everyone around my age feels the way we do about him and his voice because we were directly conditioned to it from an early age.
They're both great actors, I like both of them. I thought I would say Freeman hands down - but the more I think about it, the closer it gets.

Morgan Freeman is loved by people of all ages, genders and races.

Pretty sure Woody is respected as an actor but not loved.

This may not be a popular take but I think Morgan Freeman is the bigger star but I think Woody is the better actor. I love Morgan Freeman movies but a lot like Ryan Reynolds feel like he just plays every character the same way. That's not necessarily a bad thing either. Woody has had a good number of more diverse roles.

An incomplete Tale of the Tape

Morgan Freeman
Driving Miss Daisy
Glory
Robin Hood
Unforgiven
The Shawshank Redemption
Seven
Bruce Almighty
Million Dollar Baby
Gone Baby Gone
Batman Begins, The Dark Knight, The Dark Knight Rises
Invictus
Lean on Me
The Sum of All Fears

Woody Harrelson
Cheers
True Detective
White Men Can't Jump
Natural Born Killers
Kingpin
People vs. larry Flynt
Wag the Dog
The Thin Red Line
No Country for Old Men
Zombieland
The Hunger Games
Catching Fire
Mockingjay 1 & 2
Solo
Three Billboards Outside Ebbing, Missouri

Writing the list out totally changed my opinion to Woody Harrelson as my favorite of the two. He takes on some diverse roles. Sitting down for a marathon binge of Kingpin, White Men Can't Jump, No Country for Old Men, and Three Billboards sounds like a great night.

OP asked for biggest star, not better actor. I do agree that Woody is the better actor, but when it comes to star power, It's Freeman and I really don't think it's close.