It happens both ways in my group. For the most part my players will spend the XPs as they get them (adding a DC here, improving a Skill there, and I also require them to explain how it came about), but there have been a few times when somebody will have their eye on a new Power and save them up for a Big Bang.
Just recently one of my players spent XPs she'd been saving for about a year to buy off Limitations so that her powers were permanent instead of requiring an injection every time she wanted to use them (I guess she got tired of her GM exploiting the OIHID and Charges). I worked the change into the scenario (she accidentally ingested three vials of her 'special serum' after they'd been heated to boiling in a fight with her arch-villain), which makes it much more memorable.
That's the closest I come to allowing a full redesign: if you want to save enough XPs for a "radiation accident", then we'll do it. Otherwise, those points are locked in unless a do-over is necessary, like when moving from one edition to another.
I really like that idea of drawing up two versions of the character, Hyper-Man.