I've already had my tonsils taken out, so how bad is a wisdom teeth extraction compared to that?

Depends: Pain and swelling after wisdom tooth extractions depends on the severity of the impactions. If they are not impacted, post op in not bad. Severely bone impacted teeth can result in a lot of swelling and pain. However a good surgeon will prescribe proper meds and home care to get you thru this.

Too many variables: How old were you when tonsils were taken out? Wisdom teeth are easier in general the younger you are, but the ease of extraction also varies with the difficulty of the extraction. Individual patients also vary extensively from patient o patient. The best person to give you an answer is someone who has performed dental procedures on you in the past so they can give a treatment based comparison.