Answer: A quick growing perennial vine to cover a sturdy arbor in full sun would be Campsis radicans or trumpet vine, another possibility although it can be slow to establish, is the sweet autumn clematis, and another possibility is Dutchman's Pipe (Aristolochia durior). These three are all twining vines and will wrap themselves through a trellis type of support. They also bloom.
Unfortunately, very few vines thrive in full shade. You might experiment with the clematis and Dutchman's pipe and see if they will thrive for you, otherwise you might try the deciduous Parthenocissus tricuspidata or Boston Ivy which gives excellent coverage and turns bright red in the fall. Another possibility would be the evergreen English ivy (Hedera helix); note that these last two climb by little clingfasts or hairy roots and will climb a relatively smooth surface such as a bare post, they will also spread outward over the ground if left unchecked.
Annual vines such as moonflower, morning glory, hyacinth bean and so on will all thrive in full sun. None that I can think of would do at all well in full shade.
I hope this gives you some ideas.
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