Both of these perennials will reseed themselves all over the place. For that reason I cut mine to the ground in late September. By that time the birds have enjoyed them quite a bit, but I still will have way too many volunteers coming up everywhere in spring to 'weed' out.

I take a middle road, leaving some on and removing others so that it doesn't re-seed too much yet still provides some winter food.

I take the middle road too. I have too many seedlings of all stripes, but I don't mind these particular volunteers. I have been able to give lots away and to create big swaths of coneflowers. So I leave them up for the most part, except in areas where I want the garden to be clean to minimize the massive crunch of garden work in the spring.

I leave the echinaceas up but most of the rudbeckias get cut. All the R. goldsturm gets cut, never planted any of them in the first place and spend a good amount of time ripping the whole plants out when I dead head to control their spread.

I have a bird feeder anyway.

I love the way they look during winter...especially surround by grasses...and the wildlife in your area will greatly appreciate the seeds during winter. Yes, they will both reseed to a degree...but the seedlings are easily pulled up...so I always vote for leaving them standing over the winter.

I leave all the seed heads on and do not cut back any stems. I just let nature take its course.