Once you'd downloaded a map, it will do everything offline that it can do online.
With Onx, the biggest deficiency I've found is that it won't store offline maps on the SD card. I'm limited for space so I sometimes have to delete some maps to make room for a new one. My SD card has room for the whole state but Onx can't access it.

“In a time of deceit telling the truth is a revolutionary act.”
― George Orwell

It's not over when you lose. It's over when you quit.