The best way to understand the differences is to try it out. I haven't used either of these tools personally, so my comments are more general.
We focus on giving you an extremely rich crash report and day-to-day workflow tools, whereas often other tools are more about high-level passive analytics. Additionally we work cross platform (web, mobile, and desktop), and go much deeper than most things that simply aggregate logs.
I'm the co-founder of Apteligent. David, I'm surprised you would describe our solution as "high level passive analytics" unless you haven't tried it yourself.
I would say the difference is our deep focus on mobile user experience vs Sentry's focus on cross platform error reporting. To understand your users this also means you need more data than just crash. For example: app load times, network data, UI latency, etc.
Apologies (edited), I meant to suggest that other solutions are generally that. I definitely haven't used Apteligent (or Crittercism), but things like New Relic (which from a glimpse of screenshots, seemed similar), I would label as passive systems.
We focus on giving you an extremely rich crash report and day-to-day workflow tools, whereas often other tools are more about high-level passive analytics. Additionally we work cross platform (web, mobile, and desktop), and go much deeper than most things that simply aggregate logs.