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.