I personally dislike it, because how can you call
x-anime
y-manga's anime if it's not the actual story? I like seeing the story being told
how it was written, but in motion.
I'm not too sure what you mean by being told in a different way --99.8% of the time when animators change anything in the plot, it ruins it. Though there are different levels of change from anime to manga. Some have slightly different dialogue, which is a-okay; there can also be times when certain events are altered, ie, happening at different times-- which can be stepping on a mine, ruining it, or just sliding past,
noticeable, but not having a major impact. There are also the cases when anime completely jumps ahead of a manga, such as Kobato, and is a different story on its own, it seems.
When manga are made into anime, they aren't told the exact same way at all. The fact that one is being read and the other you watch is a HUGE difference in my eyes. I like it when the story is told in those two different ways -- manga and anime. Not story and story.
Just my opinion.