The big difference I see is that truly unpleasant and unsafe jobs will see wages rise. Being a clerk is not a great job, but it's not a bad job unless you have an awful boss. If your boss at the grocery store starts giving you trouble, it becomes much easier to just walk away and eat rice and beans for a while until you can find another job.
This is assuming we don't raise the BI in response to inflation. We shouldn't do that. (Matching or slightly exceeding targeted inflation seems a good idea; raising in response to observed or expected inflation seems potentially disastrous).
Across all sectors of the economy, lots of low-income jobs will be eliminated. If we don't have BI to protect those soon-to-be-ex-workers, we're going to have a sizable portion of population in poverty, with no skills that let them outperform automated systems.
Right now in some cities, Amazon and other services will deliver your food. I'd expect this to gain popularity as delivery costs come down and the cost of running an Amazon warehouse type grocery store would be significantly cheaper than running a traditional grocery store. This will drive down prices and will eventually run traditional stores out of business. So you're left with an automated warehouse moving your food around and a self driving car to deliver it. Shouldn't need that over prices clerk after all.
Of course, you'll still need some workers, but if their jobs are still needed after mass automation, they're probably already worth a lot more than minimum wage.
Or we'll find a way to survive with a lot fewer minimum wage grocery clerks in the future.
Sounds great to me.