I can't remember anymore how long I've been using either one of them. But, for long. Not quite as long as they've existed, but almost. To me, a MSN Live user, SkyDrive came first. I don't even remeber if it was called that back then, but who cares anyway. When it was available and came to my attention, I started using it. For what exactly, I don't remember either. It wasn't like I could've used it in my phone, and tablets didn't exist (at least not in the sense of today). But, for something.
The most important thing I tried to use it for, was to share photos between me, my mom and my sister. As for my mom, no prob. She had a Live account too. But for my sister? She's a devoted non-Microsoft person, so nope, no Live account, nor was she about to be getting one. And now, my current husband is the same way. So, so much for sharing in SkyDrive.
My sister was the one who then introduced me (and my mother, on the other side of the world) to Dropbox. I was a bit reluctant at first, mainly because it meant creating yet another account, a password to remember and all that jazz. But that proved to be the exact strenght of Dropbox. No strings attached. In order to have an account, you don't need to become a part of a Micrsoft or Apple or Google network. You just use Dropbox. And sync it on which ever devices you like to use it on.
Back then, when I made my Dropbox account and started to familiarize myself with the desktop app, with the Win Explorer folder, and the Adroid app and all, SkyDrive did not offer all that. It all came along a bit later. So SkyDrive sort of got pushed back, as a storage for OneNote notebooks (works better than with Dropbox) and later on the de facto upload location for my Lumia photos. I stored all my stuff in Dropbox, and eventually started to struggle with space, unwilling to get a 100GB plan or something.
Call me dense, call me what you will, but it was only yesterday, that I realized that I actually could just as well utilize SkyDrive for all my own, non-shared data, and leave Dropbox to be the sharing platform. For the Win Explorer folder is there, and it works perfectly with both my Lumia (duh!) and the iPad (don't know about Android, but then again, my Galaxy Tab has been reduced into a Kindle device nowadays) - and I have all of 25GB of storage space there, complimentary to the 'old' users!