Andrew Janjigian, writing on Wordloaf: Stiffed.

There's a ton of great stuff about starters in here that I wasn't aware of.

More importantly, stiff starters also favor yeast growth over bacterial growth, which means breads made with a stiff starter (particularly one maintained regularly that way) should be milder in flavor/tang than ones made with a liquid one. They can also gain greater lift and/or proof more quickly/reliably, since their yeast populations can be so much more robust.

And later on:

Liquid starters have higher enzymatic activity than stiff ones, which means they can confer greater extensibility to a dough. This makes them the better choice for breads that require extensive manipulation during shaping, like baguettes, bagels, or pizza.

I generally use a stiff starter at around 80% hydration because I've found it's easier to maintain. Maybe I should bump up that hydration a bit to see if my dough does get a bit more extensible.