These looks like flat-panel Microwave dishes, which are used in narrow band Communications links over short distances (30-50 miles). These are used for high speed internet where optical fiber is unavailable, and a cellular network/satellite is not available or unwanted.
You will notice they are both pointed in very specific directions. This is because Microwave Communications links work in a very tight radius. Imagine the dimensions of a normal drinking glass, where the 'signal' must be directed in this radius from the sending position to the receiver.
The struts on each are for reducing vibration in windy conditions, and for ensuring integrity of the band position over time. In simple terms, reliability of the internet connection.
Based on the positions, the perpendicular dish is likely getting a signal from either Great St James, or St Tomas. If its from Great St James, they may be routing the signal here then re-routing to Little St James. The other dish 45° to the front face of the building looks to be routing to another part of the island, or St John.