Both plays start with a shipwreck that takes characters to another world, so to speak. Viola shipwrecks in Illyria and must become accustomed to a new identity and new people in order to survive there on her own as a woman without male protection. Ferdinand and his entourage shipwreck on Prospero's island and become chess pawns in his game for power.

Both plays end with a reconciliation between parties, but there are tinges of the bittersweet in both as well. Malvolio swears revenge on all the characters in his last scene. The Tempest ends with Prospero giving up his magic (which one may see as a good or bad thing, depending upon one's reading of the character), thus signaling an exit from the island's otherworldly enchantment and a return to ordinary life.

Both plays also boast metafictional elements. Twelfth Night features many characters "playing" roles: Viola becomes Cesario to survive in a male-dominated world and even "plays" Orsino to an extent when she tries to woo Olivia for him. Maria and Sir Toby play a complicated con on Malvolio, pretending he is mad, which is itself a kind of theater.

In The Tempest, Prospero is sometimes seen as a stand-in for Shakespeare the playwright, controlling the other people on the island and assigning them roles in his elaborate plot to get revenge and regain power. Magic becomes equivalent to pen, paper, and the creative imagination. When Prospero gives up his magic, he is essentially giving up his role as master storyteller, thus ending the play.

Well, the most obvious comparison is that both are "shipwreck" plays.  Both plays begin with a shipwreck, though The Tempest actually depicts the shipwreck (Act I, Scene i) and Twelfth Night simply shows the results of the shipwreck, with Viola and the Captain on shore (Act I, Scene ii).

Both plays involve shipwrecked family members who go through the whole of the play imagining that their loved ones are dead (Alsono and Ferdinand assume this about each other in Tempest, Viola and Sebastian in Twelfth Night).

Both plays also derive a great deal of their comic relief from characters who spend a great portion of the play drunk -- Stephano and Trinculo in Tempest (Act II, Scene ii),  Sir Andrew and  Sir Toby Belch (Act II, Scene iii) in Twelfth Night.  In contrast, however, these drunk characters are servants (low born) in Tempest, but high born (Sir Andrew, Sir Toby) in Twelfth Night.  However, the relationships between these comic characters are similar.  Both Stephano and Toby are leaders, know-it-alls.  Both Trinculo and Andrew are followers -- silly and not very intelligent.

An interesting case for comparison could be made between Caliban in Tempest and Malvolio in Twelfth Night.  Both are in service to their lady love, and both are thwarted in that love.  Both plays end with the fate of each of these comic villains unresolved.  It is worth noting that, generally, the audience feels a certain sympathy for both characters which is almost uniformly NOT felt towards them by the other characters on stage.

Both plays also end with reconciliation in Act Five.  Those separated by shipwreck are reunited, and marriage is anticipated for the lovers in each play.