assuming "other-things-equal," 559 tires are not inherently tougher than 622 tires. Equal tire widths, tread depth&pattern, will make the 559 tire and wheel lighter. The 622 (known in its ATB incarnation as 29 inch) will roll over bumps a bit better.

Larger rim/tire diameter can be used to compensate a bit for the bumpiness of the ride you'd get from narrow tires. Likewise, narrow tires+rims can be used to (more than) compensate for the extra weight of a larger diameter rim/tire.

Much has been said about whether rolling resistance is lower if you use a large diameter rim or a small diameter rim (other things being equal) and from what I've read, the very few studies that have been done either conflict with each other or fail to show enough difference for it matter a whole lot. For bumpier surfaces, fatter tires and larger diameter rims can both, in effect, smooth bumps out some, so that less energy is lost to the bumps. Fatter tires and larger diameter rims/tires both increase weight though, which will slow you down if you have to stop and start or go uphill.

To see a really obvious difference comparing one rim size to another, you could compare rims/tires with an outer diameter of 27 to 29 inches (on 622 rims) and rims/tires that have an outer diameter of 16 to 20 inches (BMX, folding bikes, and motor scooters).

As far as "how far on a pedal stroke", the truth is it doesn't matter a whole lot what size your wheel is. If you use the same gear ratios, smaller wheels will give you less distance per pedal stroke but make it easier to climb hills. Switching to a bigger wheel is like switching to a harder-to-pedal gear, which will give you more distance per pedal stroke and might make it too hard to pedal uphill.

In practice, bikes have their gearing chosen to suit the wheel diameter (and expected range of speeds they'll be used at), which can more than make up for a difference in wheel sizes. 20 inch wheels can be set up with gearing that is too hard to pedal uphill, and 29inch wheels can be set up with gearing that makes it almost impossible to pedal yourself up to speeds higher than 5mph.