OP, let me clear some things up. I am a proud 920 owner, as well as a proud Z10 owners.
One post said they though BB was a dead platform. I think BB will be fine, at least for the length of time you will own the phone. I would not worry about the.
Apps-WP is def. better in this area. BB is in the situation that WP was back around early Spring of 2012. They have some big name apps, but a lot are missing. To those that say that all apps that are just ported from Android to BB are crap, they are wrong. There are def. some examples of crap, but I could just as easily find native WP apps that are horrible.
As far as sideloading Android apps, it is harder than you would think. You have to first get the APK file from somewhere (there are ways of getting them from the Play Store. You then have to use a program to convert them to a BAR file (which first requires getting a token directly from BB). Then you have to use another program to install it on your BB phone. I found apps that I sideloaded took longer to load at first, but then ran just fine. Currently, only Android apps compatible with Android 2.3.3 and below will work with BB. If they require a higher version, you will have to wait for BB10.2 (official current release is 10.1). There are other limitations as well. Bluetooth, for example, won't work with apps you sideloaded.
Ease of use - BB10 is def. harder to learn that WP, but not hard. It has a different flow than the other OSes. Once you get the basics it isn't hard at all. I actually prefer the way it does some things with swipe gestures compared to buttons.
Music - WP is better considering you can use a lot of the different music services plus Xbox music. That said, I do believe you can use Google Music through the browser on the Z10 (though obviously that isn't a perfect solution by any means).
Browser - Z10 kills WP for one reason: built in Flash support. I am not one of those people who believe that Flash is worthless. For example, I don't think any platform has a good Justin.tv app. They all suffer from problems. The Z10 is the only phone I can use Justin.TV from the website which is a better experience. Also, Amazon Instant Video works extremely well though the Z10 browser because of Flash. WP can't use the service at all because of no app or Flash. When it comes to video based apps, the Z10 can make up for a lot of them that are missing because of this one feature.
Camera - 925 will destroy the Z10.
Keyboard - Really good on either phone.
Multitasking - Z10 is the winner. With true multitasking (all apps are actually still running compared to WP), switching between is a lot easier. BB10 also puts open apps more in the forefront by turning the multitask selection page into the homepage.
Microsoft integration - Obviously WP is significantly easier and more powerful for this. I would say though that the z10 is better if you use a lot of Google services.
As far as the posts that talk about missing "basic features" on WP, they are missing, but are only "basic" to some people. It really comes down to what works for you. No need for me to go into each one.
It really is going to come down to what you use your phone for.
Click here to check out my review of the Z10 to get further details.