Via BEDOPS:

$ bedops --not-element-of 100% A.bed B.bed > elements_unique_to_A.bed
$ bedops --not-element-of 100% B.bed A.bed > elements_unique_to_B.bed

To measure similarity, you could calculate the Jaccard index based on cardinality of intersection and union of sets A and B.

First, calculate cardinalities:

$ AnB=`bedops --element-of 1 A.bed B.bed | wc -l`
$ BnA=`bedops --element-of 1 B.bed A.bed | wc -l`
$ AuB=`bedops --everything A.bed B.bed | wc -l`

Then calculate the index:

$ calc "(${AnB}+${BnA})/(2*${AuB))"

You can and might likely want to adjust the overlap criteria passed to --element-of to make set membership more stringent than one base of overlap between peaks. For example, you might specify a minimum of 50% overlap between a pair of peaks to call them "similar". Or you'd calculate some summary statistics about peaks and require a minimum of one SD of overlap (however many bases that is for your datasets), etc.