Are these the same jacket?

Yes. Both are the Patagonia R1 Air Full-Zip Hoody. The fabric, hood and pocket layout match; only the fit wording and listed weight differ.

Which is better for skiing?

Either works as a midlayer. The slim-fit version layers more cleanly under a shell, while the semi-relaxed cut gives more room for a base layer underneath.

Is it breathable enough for high-output hiking?

Reviewers say it is less breathable than Patagonia's claims suggest. It vents well through the full zip, but it runs warm on hard climbs.

They are the same garment, so durability is identical. The zigzag knit resists pilling better than flat fleece, and the woven hem and cuff binding hold their shape.

If you want the slim-fit version as an outer layer, size up. For layering under a shell, take your normal size.

Patagonia R1 Air Hoody vs Patagonia R1 Air Full-Zip Hoody

These are the same jacket: the R1 Air Full-Zip Hoody. The listings differ in weight figures and fit wording, but the fabric, hood and pocket layout are identical. Buy whichever listing matches the size and fit you want. Reviewers call it a comfortable, stretchy, versatile midlayer that is less breathable than the marketing suggests.

Choose the R1 Air Hoody if you want the slim-fit cut that layers cleanly under a helmet and pack straps.
Choose the R1 Air Full-Zip Hoody if you prefer the semi-relaxed cut reviewers describe as roomier through the body.

Prices

Patagonia R1 Air Hoody: $189.00 at Jenson USA (checked today)
Patagonia R1 Air Full-Zip Hoody: $66.00 at Coast & Trail (checked today)
Difference: the Patagonia R1 Air Full-Zip Hoody is $123.00 cheaper than the Patagonia R1 Air Hoody today