I have a 357 Henry single shot. Still getting to know it. But the wood is fantastic, and overall build quality is really nice. It's not 'high grade' or anything, no polished bluing; it's a matte finish that's okay, but not stunning. It seems well-thought-out and looks nice. Can't really speak to accuracy so far, but it does send the majority of my cheap plated berrys bullets 38spls into a <3" circle at 100 yards. Haven't really tried to optimize ammo or shoot for small groups though, or tried it with better ammo. I heard that they had problems with the trigger in the past, but mine is quite good - clean, crisp, and not overly heavy.
Downsides: It's quite hefty. For a 357, the barrel is sure a lot beefier than it needs to be, and I'd also much rather it came in a 16 or 18" length. As it is, the balance is front-heavy and awkward compared to my Rossi single shot .44. It's not super handy and fast-handling. The stock drop is pretty significant, and a scope mount needs to be quite high to clear the hammer - so its not a great platform for an optic; you end up with a high scope and a low stock, for an awkward 'chin weld'. I pretty much intend to get a Skinner peep on it anyway after I do some basic load work, so, it doesn't bother me. But if you want to primarily use it with a scope, you might be disappointed. The factory iron sights are okay, too.
The CVA is plastic, and has no iron sights. If you want a classy-looking traditional gun, get the henry, hands down.
I'd also recommend looking at the Rossi LWC. It seems pretty ideal as a quick light and handy 'truck gun'. My Rossi is an older model, not an LWC, but I definitely prefer it's ergonomics