There are many little changes through out the anime, form the manga. For instance when Irene gives her arm to Clare in the anime it kinda comes off as she knew she would be killed soon and/or leaving the viewer wondering how she'll feed herself, but in the manga she tells Clare that truly strong offensive warriors can regrow a human strength limb (so no using a Claymore, one handed at least). So since she doesn't really battle any more the loss of her Claymore limb wouldn't effect her and she could continue living the way she had been once her new arm was completely regrown in about a months time.
So it is rewarding to read the manga and after watching the anime. Plus us manga readers won't call you on making a mistake like saying there's no Teresa backstory.
I personally don't read Claymore to the level that I had when I first got into it, which was once though every other day
. But now I read the whole story at least once a month if not twice or three times. I read the first five volumes again, twice over in a day, since of our debate over Raki+Clare vs Clare+Teresa. Mainly since you got me thinking nonstop about them again.
I also read multiple translations of Claymore... for two reasons, first off to better understand what was said and meant in the RAW (since I can't read Japanese), and second so I never get bored with anyone translation (which reminds me I need to thank Cyclone for telling about 10Sigh's translation, it was
really good). That way I'm focusing more on the feeling of what was said rather then the exact wording of a translation.