Well, in both cases, the main characters are misfits in some way. In both cases, art and love are their two roads through which they seek social acceptance. In both cases, they end up dead. You have a good general structure of similarities.
However, you also have marked differences. Emily is warped by a lifetime of control and indulgence; her oddity is supported by an entire town. Paul's, by contrast, seems more innate in his character, and, of course, younger.
Likewise, the town fails to act to correct Emily, but the school does act on Paul. (It forces him further away, but it does act.
How they die differs markedly: age vs. his own hand.
As far as loneliness, that may be the most marked difference. Paul's entire soul breaks with the loneliness. Emily's…warps. She sleeps with a corpse, after all.