I love re-imaginings a lot better than remakes.
Those being
very iconic ones. It forces/allows the creative team to completely do their own thing and go in their own direction rather than trying to recreate the original beat by beat with only some creative freedoms allowed. Sometimes reboots are both and you can see this beyond easily where gates were thrust up - take Rob Zombie's 'Halloween' for example. The first part of that film was a very intriguing and original character study, the likes of which we rarely get to see in horror films. The second part of the film, where it becomes the classic 'Halloween' film is a disappointment in comparison, but it's not hard to fathom a guest why. In the first part, Rob Zombie was allowed to go crazy and do whatever he wanted - in the second part, he had to turn in a remake.
I'd say superhero film "do-overs" are more akin to re-imaginings than they are to reboots as well since the creative team behind it isn't aiming to do the same old original story - rather taking an idea in a completely new direction. Although it gets into trickier grounds here. I'd say Nolan's Batman films since the go against the grain and against the execution of every Batman film prior, he didn't just aim to update it - he aimed to completely revolutionize the way superhero films are approached in terms of favoring reality over stylization and "camp" (for lack of a better term). On the other hand 'The Amazing Spider-Man' I'd say is more of a reboot since it had in general the same basic approach and it told the same exact story basically just with a different villain.