比起 + [B] + (来),[A] + [adjective / verb phrase]
[A] + 比起 + [B] + 来 + [adjective]
比起 + B names the yardstick, and the rest of the sentence says how A measures up against it. B usually opens the sentence, and 来 can follow it.
The second half is often 更 + verb, for a preference.
A比B puts both things in one tight clause with the adjective last. 比起 gives B its own clause, which leaves room for a longer comparison and for 很 or 已经. B can also be a whole activity.
比起 can also sit in the middle, after A, with 来.
English can tack "compared with B" on at the end. 比起 + B goes before what it's compared with.
The thing after 比起 is the standard, not the winner. 比起他,我高一些 means I'm the taller one.