The simple fix would be to set a piece of base at an angle to connect both tops. and notch the bottom edge to go over the difference in the floor. The profiles at the top are pretty close to being the same profile and can be "faired in" together by a little finesse by sanding. The difference in thickness does not look to be that much different to be a concern, it will just need the protruding edge sanded flush and painted, done it many times with material 1/8" thicker than the other.
Another way is to remove the shortest piece of base on the high floor side and rip it so it is not as high to get the tops level with each other. Sometimes the difference is so great from one piece of base on one side of a door to the next piece on the other side of the door, (this is where I have made the transition in most of my cases) reduce it a slight bit less in the same room so the difference is not so noticeable right off. This may have not been the best way to explain it. I have also used taller base to do the same thing.
The way I would fix this situation is a takeoff on Jimmy's answer, but taking it to a different finish.
Remove the corner molding all around the opening, measure the width of the wall from finish wall to finish wall, (1X6 may do it, most walls are 4 1/2"-5" wide) to get the width a new jamb. Rip the material to fit the width of the wall to reline the the opening in 1X material, notching the bottom of the new jamb to step down over the different levels of floor, and if needed cutting the transition strip back 1/4" more to make room for the 1X material. After that is set, get door casing and trim out both sides of the wall, cutting the base shorter to allow the base to finish at the outside edge new applied casing which will allow the base to terminate in a place that will not be visible at the opening.