On the one hand, Archaeopteryx could probably blend in and just look like a bird that they put together a little wrong until you got up close and realized its actually a freaking dinosaur. I bet they had a mean bite, but alas, they were neigh but a kilogram (2.2lbs) and just a wee tad over a foot (30cm) if you stretched them out long enough.
On the other hand, Archaeopteris is a tree, and not just any tree, but one of the FIRST trees. Early Trees are the only beings besides Humans that are personally responsible for a Mass Extinction, so that could be kinda badass depending on how you look at it or just depressing. They reproduced through spores, which is really cool. Especially since their closest living relative, Clubmosses, can have their spores used as flash powder to explode stuff and magic tricks.
Its a tough call. Realistically, I could see the Archaeopteris falling and crushing the Archaeopteryx, but then they'd be lose. I dunno what kind of a diet Archaeopteryx prefers, but if they eat plants, I guess technically they could eat an entire Archaeopteris, but it'd take a shitload of them seeing as they only weigh a kilo.
Archeopteryx (Is it just me, or does its face kinda look like the sicko guy)
Archaeopteris (Its tougher to find a photograph of these guys that makes them look adequately cool, but trust me this one doesn't do them justice even though its the best i could find)
Based on the skull/teeth, archaeopteryx was almost certainly a carnivore. If you give it the benefit of the doubt and assume it would even try to eat the tree, it still wouldn't be able to consume that much food or even pierce the proto-bark.