IMO the 55-250 IS and 70-300 IS are both fine lenses for casual use. If you're after the best image quality possible the 70-200 f/4 L is a better choice, but it comes at the expense of no image stabilization. If you go with the L lens you could find yourself in a position of having to bump ISO beyond where you want to go, or be forced to use a flash, to avoid image blur in less than ideal light.

I don't have the 70-300, but do have the 55-250. I've tagged all my pictures in Flickr with which lens is used, etc... My 55-250 pictures are at the link.

http://www.flickr.com/photos/68255851@N05/tags/55250/

Dave