It all started with a hint. Joss Whedon was considering using Scarlet Witch and Quicksilver for his highly anticipated followup to the biggest comic book movie of all time. Weeks after he confirmed it, Bryan Singer revealed he'd be using Quicksilver in his highly anticipated return to the X-Men franchise. A line was drawn, shots were fired, and the race was on.
Mega-studios Marvel and Fox were both courting a character that had previously been unknown to the general public. Now he was the most sought after free agent of 2013. Some might say Fox's hasty casting of Quicksilver was a direct jab at Marvel, while others can argue he has just as much, perhaps even more of a right to be in an X-Men film than an Avengers one. A legal battle over rights insued, and in the end, with a decision that made us ALL winners, BOTH companies were allowed to use the speedster.
But not without some guidlines, of course. There can be no overlap, so X-Men could not mention Avengers 2 and Avengers could not refer to Maximoff as a mutant, or as Magneto's son. Fair enough. (Well not really- for comic book fans this was equal parts complicated, confusing, and annoying.) But the bottom line is, both movies were going to get to complete their visions.
***SPOILERS for X-MEN and AVENGERS 2***
So how did these versions turn out? Days of Future Past invisioned a kid that who's life around him just can't keep up. He steals for the fun/ease of it, and is commissioned to break Magneto out of a high security prison. What follows is perhaps the scene-stealing setpiece of the film, while also making a inside joke about Erik and Quicksilver's relationship. At the end, we see him cradeling his baby sister, and assumed Scarlet Witch.
Age of Ultron correctly makes Pietro and Wanda twins, and even with the backstory changed, the destruction of their home as children, which turned them into villains, still basically works, and is in line with some versions of the characters. No Magento needed. This Quicksilver is a little more henchman like, though; the muscle to get the job done. No standout scenes like the X-Men version, but he is in the movie much more, and has a fun rivalry with Hawkeye.