Intersect, or Union as Aaron mentions, are Overlay tools that should get you a set of polygons that have attributes of both. Identity is also an option if you have an Advanced license, and is probably the most suitable for your end goal. Basically you want to cut up land use polygons if they cross a catchment boundary and then assign the catchment id to the resulting shapes while preserving the grazing/irrigated attributes.
Note that Intersect only returns areas of overlap, Union returns all areas from both layers, and Identity will return all areas from one layer but cut up according to the other. The attribute format/output from each tool varies and one may better suited to your problem.
Once you have have the new polygons, you can run Summary Statistics on the attribute table using catchment ID and whatever the grazing/irrigated attribute fields are called as CASE fields (note field order matters to resulting table), with your area field as the STATISTIC field using SUM type. This gives you a table with a breakdown of catchment, pasture type, the number of polygons that comprise the unique combinations of those two attributes (frequency), and the sum of the combination's total area.