I do the same... except that in most cases, if the same software is available on both MAS and Developer site... I prioritize the MAS first.
My rationale: In most cases, it vastly simplifies updates. Non MAS software mostly checks for new updates when you launch the application... which for convenience, is the absolute worst time to perform an update... because it is exactly when you want to use the application. Microsoft Office updates frustrate me the most... because they are usually somewhat slow updates.
I do it the other way, order via developer first and only via MAS if no other option or if this is the best option. Ordering via the developer allows me to first use a trial version and register it if I like the app. It allows me to get discounts when upgrading to a newer version, when buying another product, when buying in bulk and/or when buying a bundle pack (say app a + b + c or OS X + Windows version). That means that it is a lot cheaper to get things directly from the developer.
Updating the MAS also comes at an inconvenient time but the advantage is indeed that you can hit 1 button and update everything at once. When buying apps via the developer you need to go through them all 1 by 1. However, you don't have to continuously check for updates because the apps and the app store do it themselves. They'll bug you about it and you can either go ahead and install it or simply ignore it till the next time. You can pick your own convenient time

The MAS makes this a bit easier though and can even do it automatically (which is not to be recommended since crappy updates are also installed which can render the app useless). There are 3rd party apps that do this for non-MAS apps as well (MacUpdate has one for example).
The biggest problem is the update intervals of the MAS. They have to be reviewed first and can be rejected. Via the developer you are only limited by their speed. This has led to security updates and bug fixes being brought out much quicker for non-MAS apps. When you have a zero day exploit that is already being actively exploited speed is essential.
A second advantage of the MAS is that the software is generally easier to share across multiple computers and family members. Most MAS software also supports family sharing, which makes it more economical if you have several family members who need the same applications.
That depends on the license. Lots of apps already had a license that allowed you to install it on every machine you control/own/work on, some have introduced this after the MAS. There also equivalent licensing that allows you to use it on up to x number of machines. I've seen licenses from non-MAS apps that are much better then what the MAS offers. I get to use it on my work machines for example.
MAS does allow for family sharing but only if the developer allows it too. In reality not that many apps are allowed to be used with family sharing plus there are lots of other issues with family sharing itself (simply put: it is not working). If you don't have a family where you want/can share the apps this is useless anyway.
I have mixed feelings about the MAS. It can be quite convenient but it can also be a very very inconvenient place. Especially when it comes to upgrades and bundles. Apple really needs to fix those things and add a trial function to it as well. Microsofts store is better in that regard.