DRO vs HDR
Both DRO and HDR share in common that they are ways to handle wide ranges of brightness. They each have their pros and cons:
DRO requires only a single image from the sensor, so shots are fast to take, and fine for scenes with movement, unlike HDR.
Photos will still take longer to process compared with Standard photo mode, but it will still be faster than HDR.
HDR will in general be better at scenes with a high range of brightness values. It can take advantage of the information from three separate images, rather than reprocessing a single image.
DRO is available on both old and Camera2 APIs (though it still requires Android 5.0).