Angel/Archangel is just the latest example of a duplicate character within the franchise (others so far being Jubilee, Moira, Emma, Sabretooth, Toad, Deadpool, Psylocke). There is a weird tendency for re-imagining characters, and this is partly because many of them weren't done right the first time (they were shoehorned into minor roles or were poorly depicted).
In fact, this new Angel will be the third incarnation considering Vaughn was daft enough to put a female Angel in First Class.
On the one hand, maybe they will do more justice to these characters than was done previously. They're definitely not trying hard to adhere to what the previous films have done - Singer even contradicted his own X1 hints of Magneto/Xavier origins when he wrote First Class.
Yes, all this recasting and whatnot means the franchise timeline/continuity is a little messy and convoluted. Our main film writer at work commented on that after seeing The Wolverine and DoFP. He felt the films leap about in time too much and are not simple to follow.
The mainstream won't care about a new Jubilee or Psylocke because those were very minor roles they won't remember, and I never heard any mainstream viewers (non-geek friends, people at work, etc) make complaints about duplicates of Emma, Moira, Sabretooth or Toad. Whether they remember X3's Angel more clearly and are thrown by this new version is difficult to say at this point.
I've no doubt Singer couldn't resist the contrasting elements of angel/demon in putting Angel in DoFP alongside Nightcrawler. He loves his elemental opposites (fire/ice with Sunspot/Iceman and Iceman/Pyro and Azazel/Emma Frost... and beauty/beast with Storm/Nightcrawler in X2). We could have waited to get Archangel in the next movie, but since when have they ever waited? Deathbird would have been good (and a great set-up for Shi'ar) but to fans might seem like an odd substitute for Archangel, so why not just put him in where he belongs in comic book terms.
X-Men Apocalypse could still be a great film but the threads of continuity are fairly thin and tattered by now that you either create constructs of fanboy logic or just kick back and go with it and treat each film on its merits.
I hope they make it so Angel deserves to be in the film and that it isn't too much of a head-scratcher for casual viewers who remember the version in X3.