AFAIK here is a "duty of loyalty" that requires you not to compete with your employer so working for a company that directly competes with them would be out. Like working for both Waymo and Uber self driving cars at the same time "as an employee". As a contractor no such standard exists.
That's an oversimplification. Uber could just as readily add an exclusivity provision in an independent contractor agreement as waive (or strengthen) any default duty of loyalty in their employment contract.
The fact that this question is practically speaking unilaterally up to Uber and not the result of any meaningful negotiation between the parties makes the relationship even more employment-like, as there's usually much less negotiation around terms of employment (certainly some still happens) than in true independent contracting.
What's more, it's not clear to me that courts would enforce the duty of loyalty (and maybe not even an express contractual provision depending on the state) against a part-time rank-and-file provider of comparatively unskilled labor, just as they wouldn't prevent a 20-hour-per-month sandwich shop employee from spending an additional 20 hours per month at a different sandwich shop in parallel. Maybe a guarantee from Uber of full-time pay would change that. I believe a federal trial court has even ruled that non-fiduciary employees in California have no duty of loyalty, though I don't know if that was overturned on appeal or whether state courts have agreed.
