I have the option to choose between iOS and Android when I start my job. I have minimal experience in each so I don't have a strong preference.
Which platform would be better for my career in the US? Is demand for iOS engineers higher because iOS users typically pay more? Or does platform not really matter much?
Short answer: Pick the one that matches your personal device.
Longer answer: You want to match your personal device for many reasons:
Here's a good thread about picking up Android: "How can I get really good at Android?"
Here's a good thread about picking up iOS: "Good resources to learn iOS app development?"
Here's some notes on Android and iOS from both a US perspective and a platform perspective. I have worked on both with 10+ years of experience on Android and 3+ on iOS, so I have a lot to say:
Zooming out, you should figure out if Duolingo values Android or iOS more. This is relatively easy to test: Try Duolingo on both an Android phone and an iPhone and see which app feels better. If the iOS app has more features and UI polish, it's clear the company values iOS more.
If I had to guess, Duolingo is more iOS-focused. Very few companies are Android focused with Meta being one of them (this is actually one of the reasons I joined Meta).
In addition to Alex's great answer, I would recommend two more inputs into the decision:
Take a look at this masterclass as well, which discusses the broader topic of team selection: [Masterclass] How To Choose A Good Company And Team As A Software Engineer
Everything you need to learn about native iOS and Android is already provided by Alex and Rahul.
I'll give you my perspective as a Tech lead in one of the Big Tech companies. I have been doing Android for over 10 years and roughly 6 years ago, I was exposed to React Native. I hated Javascript before learning React. My mentor advised to me have a diverse perspective and look at each framework as a tool to get my job done.
I learned React native - became an expert at my company eventually. After moving into Big Tech, that skill of building product on both platforms helped me greatly. I would also encourage to get your native app fundamentals right on at least one platform before trying cross platform work.