Let's consider the incentives in each case and how they enable you to distribute your trust. Apple is a for-profit, publicly traded corporation. Their purpose is to make money, and they will likely do whatever they can to achieve that. More importantly, only they can see their code, not you and not other users. All you can possibly have is their word, and they will say whatever it takes to sell you their product. If they lie or exaggerate, there's no way you or anyone else could know.
On the other hand, open source projects come in all shapes and sizes. Generally, they have a strong community of both developers and users around them. If you don't feel like looking at the code, you don't even have to trust the project itself. You can look to the community and its abundance of users, at least a few of which have audited the code and share your use case. And these users aren't just neutral third parties. Nay, they're better than that. They, too, value their own privacy, and are therefore motivated to protect it.