Extreme, extremity are comparable when they mean the utmost limit or degree of something.
Extreme usually applies to either of two limits which are diametrically opposed or are as far removed from each other as possible.
The term may, however, when used with a verb of motion or one suggesting movement, imply a definite direction and therefore denote the utmost limit or degree in that direction.
Extremity, on the other hand, usually implies the utmost removal from what is reasonable, sane, safe, tolerable, or endurable. Often the term applies concretely to the state or condition of one in extreme pain, grief, anxiety, suffering, or poverty.