THESE ARE TOTAL GENERALIZATIONS. READ AT YOUR OWN RISK. Oh yeah, and I don't hate either group.
OK, now that's out of the way lemme see what I can do here... first of all, Goths are interested in the romantic, the Edgar Allen Poes and H. P. Lovecrafts and such. They're usually also big on horror. Ravens, black butterflies and moths, graveyards and such are good motifs. Photography is a bigger Goth thing rather than Emo thing (except for self pictures). Black, white and sometimes another colour like red or dark purple are the usual. Jewellery is crosses, bats, spiders, spikes, etc. Music ranges from dark classical to heavy metal, and can even overlap(!). Goths are usually without feeling, and don't complain (except in poetry).
Emos are a very huggy bunch, all about feelings rather than the lack of them. From a distance you can tell them from Goths because Goths look like the walking dead and Emos look like a walking rainbow. Black is still a big part, though, making the bright colours look brighter in comparison. Checkers are a big thing rather than lace or nets, although some do wear nets as well. Tight pants are popular. Self-pictures, usually with some Photoshop filters, are a telltale sign. While a Goth usually can't stand cute things, Emos love them. Cute pets, cute stories, cute dinosaurs, cute chibis (Emo kids may be big on anime/manga as well), you get the picture.
Shared Characteristics: butterfly jewelry, wearing black, dyed hair, feminine-looking men, preoccupation with feelings (or lack thereof), emotive poetry, Tim Burton films, striped things