Which will be most directly applicable to a career in AI drones or industrial robotics, electrical engineering or mechanical engineering?

Both are crap. Go for civil engineering. Modiji through his ultra manifesto promises a solid future for civil engineers.

In very general terms a ME tends to do more spatial work than a EE, at least on a scale that most people can understand. A career in either will be as rewarding as you make it. Each has great opportunities in the current market although I think ME has a slightly broader scope. Although that could just be because that's my field so it's easier to see the opportunities there. Also in the age of the internet, electronics and most of the principles of EE can be learned online for free. That's not to say a EE degree isn't worth getting just that unless you really want to focus on that side you can learn a lot of the same skills outside of the school setting with a relatively low barrier to entry. Regardless of what discipline you're in you'll find that engineers in general tend to have similar thought processes and outlooks. If you aren't sure what major to choose (a double major is possible but will take more time and money). But, for particularly taking interest in Industrial Robotics, it doesn't matter whether you pursue EE or ME.

Have you given any thought to Mechatronics engineering?? In any case, you can start off with mechanical engineering, and through masters, you can specialize in mechatronics.