They're both lugged steel frames, made of quality tubing. The Cheviot is made in Taiwan (at a very good shop) and the Pashley is made in Stratford-upon-Avon, UK.
The differences will be in the frame design, and the components equipped.
The Rivendell Cheviot probably has longer chainstays. That's Grant's latest favorite design feature. Supposedly, it gives the bike a cushier ride.
The Pashley is a true, traditional mixte frame, with two smaller diaga-tubes. Whereas, the Cheviot has a single diaga-tube that splits into stays at the seat post. The Cheviot design is stronger, but the split mixte stays on the Pashley are quite lovely.
Due to these differences, I'd expect the Pashley to flex a bit in the main frame, and the Cheviot to flex a bit in the stays. Of the two designs, the Cheviot is more stout but may still ride as nice.
The Cheviot has other unique design quirks. The name is funny (and spelled differently on either side), the headbadge and lugs are gorgeous (with a couple filled-in windows), it has a kickstand plate (helpful), it has a pump peg, and comes in a couple color choices.
The Cheviot also will fit wider tires than the Pashley.
The Cheviot is sold as a frame/fork, and components are all chosen separately. So, you can spec whatever components you want with any type of drivetrain.
The Pashley is sold as a complete bike, with an 8-speed Alfine Internal Gear Hub (IGH), and nice accessories like a Brooks saddle and fenders.
The Cheviot will be more expensive in the end, but you build it exactly how you want.
The Pashley is less expensive, but has a nice build on it (if you want an IGH). The price will be about the same if you decide to swap out a bunch of the Pashley parts.
Disclosure: I own two Rivendell frames, and they each have a wonderful ride. I'm obviously a fan of Rivendell, but Grant's recent direction toward stouter, upright-riding, longer frames doesn't fit my riding desires.
Though, it sounds like these new designs would work well for your desires.
I'm younger and prefer sportier drop-bar bikes, so I have a '97 Rivendell Road Standard and a '10 Roadeo.