Why "broad" instead of "large" cross-immunoreactivity?
Broad means wide as in a wide range. Normally, antibodies have one epitope they recognize, i.e., one specific target; they are said to have a narrow range of targets.

Some antibodies, however, recognize multiple targets, i.e. the number of targets they recognize is larger and their target range is widened. They are said to have a broad cross-immunoreactivity.

A 'large' cross-immunoreactivity, however, is ambiguous, as 'large' can also imply 'large reactivity', and then 'large' becomes synonymous to 'strong'. Wide is unambiguous as it always implies a large range.