Another possibility is that this is a complex query, and type conversion takes place via the = operator for each row. LIKE slightly changes the semantics, so type conversion should not be very dependent on execution planning. I would suggest that your colleague take a look at the execution plan with = in place and see if there is something like
CONVERT(varchar, variable) = othervariable
at run time. In the wrong circumstances, one type method can slow down a request by two orders of magnitude.
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