In many situations it is desirable to identify the direction of arrival (DoA) of an incoming signal. Recently the idea of compressive sensing have been applied to DoA problems using sub-sampled linear arrays of omnidirectional antennas. In this paper we explore DoA estimation with compressive sensing using antennas with diverse and reconfigurable patterns. Our results show that compressively-sampled arrays using pattern-reconfigurable antennas may meet or even exceed the accuracy of traditional DoA arrays as well as static compressed arrays of comparable size and complexity. Furthermore, we show that for arrays with lower number of elements, the degradation in performance of a compressive array can be mitigated by including pattern reconfigurable antenna elements.