Mine came shod with 40mm Marathons front and rear, with mudguards to suit, and I've seen no reason to change to anything else[1]: I might get a puncture a year, and they come on and off the rims without drama. They've got enough tread pattern to cope reasonably well with the type of unsurfaced paths that you might sanely ride a recumbent tourer on. In combination with the suspension, they're pretty much immune to badly maintained roads (just watch out for tramlining). They're relatively heavy, but it's a Panzerrad touring bike with a lardy rider, and I have much better candiates for weight-weenieing.
(My DF touringised (rigid) hybrid is shod with 40mm Marathon Duremes[2], for broadly similar reasons. I reckon 32-40mm is about right for a touring bike that can be expected to do some mild off-road occasionally.)
In comparison, I have an Optima Baron low-racer (no suspension) for going fast[3] on, especially when corners are involved. I've got 28mm slick tyres on that, and the ride is often what I'd describe as "brain-rattling". It's a joy to ride when the road surface is decent, though.
We've tried several different tyres on barakta's ICE Sprint (tadpole trike, 20" wheels, rear suspension only). It's currently wearing 50mm Big Apples on the front (because lunar road surfaces) and a 35mm Marathon Plus on the back (because hub motor means removing the wheel is a faff). We've also tried 35mm Marathon Pluses all round (hard work without a motor, very harsh ride, admirably low puncture rate) and 35mm Kojaks all round (much faster rolling, makes the handling a bit more dynamic, reasonably comfortable ride if you find the sweet spot for pressure, no grip whatsoever on mud).
Tyres are a bigger deal on trikes, because they have more of them to slow you down, you can't always avoid all the sharp stuff and potholes, and you're being rattled in two different axes. I don't think there's anything particularly special about the tyre requirements of recumbents, other than the more exotic wheel sizes, and that suspension means you can do the Moulton thing of running a wide tyre at relatively high pressure for reduced rolling resistance.
[1] They changed the design of Marathons a couple of years ago, so the tyres themselves have evolved to be slightly faster-rolling and a bit less grippy on slimy tarmac, which I'm not overly thrilled with.
[2] They were cheap at PlanetX. Width is an improvement on the 28mm Marathons they replaced, no punctures so far, rolling resistance seems underwhelming.
[3] Faster on average, and when cruising on the flat. While it's less aerodynamic, the Streetmachine easily wins on maximum downhill speed, because the immunity to crap road surfaces fends off TEH FEAR
