In the U.S. (I can't vouch for what occurs in countries other than U.S. and Israel. That includes not understanding what occurs in Canada, which is my northern border neighbor.) the change is decided by Agudat Yisra'el. They base it on a combination of what would be a "reasonable" vasikin and hashkama minyan time for most people in the U.S.
In summary, here are the primary factors:
There are people who like davening vatikin - i.e. the goal is to begin saying the Amidah exactly at sunrise. It doesn't matter when sunrise is - these people want to be there. Others, like the hashkamah minyan. These minyanim tend to start at a fixed time, say 6 AM. They are mainly geared for commuters who are on a tight schedule to, say get a train or a ride that leaves at a specific time - same schedule each day. (You can see that the goals and focuses of vasikin and hashkama are very different.)
The problem is that getting the best time frame is challenging. Daylight time pushes sunrise ahead an hour, thus making vasikin "later" than it was. If vasikin starts at 7 AM, you're probably going to get all those people moving to hashkama and you won't have enough for a vasikin minyan. On the other hand, there's also a minimal time when you are allowed to daven shacharit. So, if you made daylight time too early in the winter making sunrise at 8 AM, the 6 AM hashkama minyan couldn't run either, so everyone would have to shlep their tallit / tefillin to work and either daven by themselves or lose time from work to find a minyan near work - not that likely for many people.
In short, they have to find some proper balance to accomodate both forms of minaynim to make the majority of the population in Jewish cities in the U.S. happy. So, the scheduling seems to be based on a best average of the times needed in the U.S. to do it. That's why they determined the 2nd Sunday in March to be the best time in the U.S.
I'll have to research a bit what goes on in Israel, so after I ask my friend, IY"H, I'll edit that in.