In our gardens, petasites (often referred to as pestasites) has been a true pest. We received a number of pieces about ten years ago, discovered its true nature and eradicated it. About 4-5 years ago, it turned up in an old compost pile. It's magnificently ugly, with great cauliflower-like flowers which appear suddenly, early in the spring, and look as if the earth is being conquered by strange, vegetable-like creatures from another planet. Flowers appear before the foliage. The leaves are large, pale green, but often look bedraggled by the middle to end of the summer.
My sister-in-law grows it to her great joy in a small, city garden where it has colonized a dry, shady location. The dryness has curtailed its spread.
There is a variegated version, which is quite beautiful, and apparently less vigorous than its parent. My own personal jury is still out on this one.
I also planted Darmera in my shade garden at about the same time. Flowers appear before the foliage, are pink and do not appear over a long period. They are prettier than those of the petasites. The leaves are pleated, deep green, with an interesting texture and do not become bedgraggled by the end of the summer.
We have moved the darmera to where we hope is a better location. I would not be surprised to see it attempt to overtake the area where it was previously planted. I do find many so-called invasive plants become much, much more vigorous if hoed, dug, etc.
My choice would be for the darmera. I am also very fond of Astilboides tabularis - assuming you like big-leafed plants for moist, shady areas.

I grow both. The petasites patch is about 20 years old. One plant has turned into a patch that is 12 feet wide and 20 feet long (I have the room). The flowers are really early and weird and short-lived---and they can poke through 4 inches of snow. Under right conditions, like mine in the misty mountains of coastal Oregon, they get seven feet tall with leaves 40" in diameter. The leaves tatter very easily for no apparent reason, especially those on the outer rim of the patch, so I remove them.
My darmera grows just outside my koi pond next to a weeping red japanese maple. Nice contrast. Leaves about 6" across. Spreads slowly like iris tubers. Collect seeds by holding a large bowl under the ripe pods and giving a good shake. Seeds are a little smaller than poppy seeds. They germinate easily. Darmera easily the better mannered of the two, and will take longer exposure to direct sun. Petasities gets sunburned. Darmera is the well-mannered winner, unless you have at least half a shady moist acre.