The reason Qualcomm is behind Apple in CPU's is that they are now doing semi-custom (changing some parameters) designs based off of ARM cores.
The issue with that is simple, ARM designs their CPU's to be used in many different markets, i.e., they aren't designed specifically for mobile. They are meant to also be used in markets where parallel processing is VERY important. What this means, is their CPU cores are meant to be more simplistic (lower SC performance) but also more power efficient so they can have many more cores in CPU which is very beneficial for heavily parallelized (performing lots of calculations in parallel for example) tasks. So what you have is a processor that can perform adequately in mobile, but also perform very well in applications that require power efficiency, but also need to crunch a lot of numbers.
Here's the issue: In mobile, the biggest issue is the simple fact that it's hard to create an application that puts equal loads on all of the cores. What I mean by this, is some tasks in a mobile applications will take more processor time than other tasks that you may send off to another core. This means that although you can write multicore apps, you're much more likely going to run into issues where tasks running on core 2, needs information from tasks running on core 1 which creates a bottleneck. This isn't an issue if you are primarily crunching numbers that don't depend on each other, in those cases, the ARM cores would be much better compared to Apple's cores.
Until, Qualcomm, or someone else, starts making cores that are specifically meant for mobile (i.e. fewer but more complex designs with higher SC performance), then they will be behind Apple in mobile performance.
TLDR: By nature, it's very difficult to make mobile apps use all cores equally which means ARMS proprietary designs that focus on efficient multicore performance is not optimal for mobile use. This works very well when you have a lot of simple threads that, but it's not as good when you have very heavy threads like ones you'd expect from things like video editing.