Dragon-lite and dragon-like. Experienced players know to fear dragons, new players think they should fear dragons. I like to throw in a caveat at the beginning of my games that not all monsters in my games will perfectly resemble the monster manuals incarnation - thus, dragons may not always have 4 legs or be highly intelligent plot devices. So when a wyvern shows up in the story with players in the 2-5 level range, they get fairly anxious about what it actually it.
Wyverns do a great job of teaching players how to use their equipment/skills/magic to greatest effect. They also serve as great additions to combined arms encounters. Being large creatures with feats such as grab, rake and fly-by attack allows me to get creative in what I do to the party, like disarming a polearm or bow. It's often inevitable that at least one player has chosen a small race and that's just a grab, gain altitude and drop sequence waiting to happen. The look on players faces when a wyvern has grabbed the little person and gained about 30 feet of altitude is priceless - do they try to shoot the wyvern out of the air or try to catch the precious cargo on the drop?
But combined arms is the most fun place to use wyverns. Giants, ogres, ettins and even goblinoids work great for setting up a wyvern fly-by or a wyvern fly-by sets up a ground assault perfectly. In one game, the PCs had set up an extremely elaborate trap for a pair of hill giants - they didn't bother to check to find out if there was anything else assisting the giants. So the half-dragon paladin acts as bait to sucker the hill giants into the kill zone. The hill giants (not because I knew what the players were planning) decided it was a much better idea to have the pet wyvern just go fetch the juicy dinner for them - result, one very squishy half-dragon paladin.
In a previous post, I indicated that I don't like having one poison type per monster, so as with snakes, spiders, scorpions, I randomly decide what type of poison a wyvern has. Yes, I know this is a house rule, but why should a wyvern in one world or region have exactly the same everything as a wyvern in a different world or region. Diversity is why we have cougars, panthers, jaguars, cheetahs, lions, tigers, bobcats, ligers, tigons - yes, they are all big cats and all have mostly the same attacks/damage/hit points, but there are differences. Embrace those differences to give your campaign a unique feel.