If privacy and app permissions are your priorities, you'll be better off with an iPhone. You'll have more extensive control over each app's permissions, and from a privacy standpoint Apple's walled-garden approach gives you a highly curated emailing, text messaging, and online storage environment, plus automatic backup and restore features that just can't be duplicated in the same way with our Android devices. Of course that's all based on if you trust Apple as a corporation and you're willing to sacrifice personal choice over managed oversight.
But currently the entire smartphone market is dominated by Android and Apple, and for all the verbage about free market competition, it's definitely not. All the minor players trying to get a foothold in the mobile device market have a massive uphill battle to gain even a tiny percentage of market share. So yeah, there might be an isolated, security-focused phone that comes along but at this point it may or may not survive past a few years. Even a big name like Blackberry, a well established brand with a solid user base had its day. Its Blackberry Enterprise Servers were a well-respected cornerstone for secure services, and now for various reasons Blackberry is just another footnote in smartphone history.