Adjustable desk owner here as well - while it's great and I wouldn't want to miss it [1], I also have a bar stool with a backrest, so I can easily transition between standing and sitting in a second. I also often find sitting conducive to thinking, but then again sometimes I feel most focused when walking around the room.

It's hard to put my finger on what it depends on exactly, but it seems to me that often when I have no idea how to approach a problem, I like to sit or lie down, roll it around in my mind, maybe look at the code/the application and let possible solutions come to me. When I already have a basic idea of what direction to go in, I like to walk around in front of my desk while I work out the details (= talk them over with myself) and then type/write standing.

It almost seems as if the natural action for a physical destination (not standing around like an idiot until I know where I want to go, then starting to walk and finding my way there as soon as I do) helps with the corresponding thought processes involved in reaching a purely mental destination.

Regarding the physical aspect - over the last years of transitioning to and experimenting with a standing a desk I have had phases where I spent hours standing, phases where I went back to sitting most of the time and phases where I had a balance between the two. My personal experience seems to match the anecdotal evidence I've encountered as well as what seems to be the scientific consensus (oiling of joints and lymphatic circulation both rely on movement, among other things), which is that the human body simply isn't designed for spending long periods of time in a single static position.

Spending hours standing tends to hurt my feet and knees, spending hours sitting makes my back unhappy. Constantly switching between the two and walking around the room in between makes long sessions of working on a computer much less taxing on the body by far and it makes perfect sense to me that the accumulative effect of this over the course of years and decades will make a difference to my quality of life down the line (in addition to the immediate effects I'm experiencing often after only a single day of doing one or the other).

Another thing I've noticed - giving myself the option to easily switch positions, forcing myself to do it for a while with a timer and paying attention to how it feels, lead to me being aware of becoming restless in a single position after a while and noticing the beginning discomfort in parts of the body, which I only used to notice when they were already hurting after hours standing or sitting.

I don't use a timer anymore, by now I just listen to my body telling me when it's time to move my arse and it all syncs up nicely with the different mental states I move between during work.

On a side note/quick rant - how stuck are we in our heads and screens, how detached are we from our bodies and how ignorant of the fact that in evolutionary terms we were moving around all the time until like a second ago, that we need a study to figure out that hey, maybe sitting on our collective arses 90% of the time might not be great for us and are we really sure that's a problem, maybe we need more studies. End of rant.

TL;DR - get an adjustable desk and a comfortable bar stool, don't stand still, pay attention to how you're feeling - both your body and your mind will thank you.

[1] IKEA has this cheap manually adjustable option if one doesn't want to spend the money on an electrical desk, plus only having mechanical parts means it's less likely to break/easier to fix if it does:
http://www.ikea.com/us/en/catalog/products/S29084966/