There's a few schools of thought on trim. Ultimately, unless you are restoring, or replicating for historic purposes, the client is always right. Of course, advice and suggestions can be made, but taste and likes/dislikes are a personal thing.
Commonly, shoe follows base moulding. Trim done without shoe may require scribing the bottom of the base, which I really don't like to do, but have done it.
In this case, I don't care for the curved transition. I would rather see a ramp type transition. I believe it would be less obtrusive, and actually a safer transition for traffic. My opinion would be to use a base moulding that has an acceptable height that when it installed on the left side, is still tall enough on the right side to look in proportion. For example, whatever the transition is, add to the dimension the height that would look good on the right. That would be what the overall height of the base on the left.
I would like to see just the base scribed to the transition, or have it installed before adding the transition. At least if the transition butts to the base, it can be replaced more easily.