Log cabins are very forgiving, at least in how I do them. I like very scrappy, and I do not worry about precision. They end up looking fine to any but the most critical quilter's eye. I'm pretty sure I have at least one lc in my photos posted here, if you care to go look.
I don't use uniform widths of strips, and there is variation in width in the rounds-- To me it's more important to have even distribution of color/value. I leave my strips long and do assembly line piecing, then trim and press. I don't square up my blocks until the final round, which is where I use a wider log-- allows for more aggressive trimming if need be. I do prefer relatively narrow strips, as I feel that makes for a more pleasing design, and because, frankly, I tend to use my less lovely fabrics up in log cabins, and they do best when you don't see huge stretches of them. So to me, narrow strips means cut 1" up to 2.5", finished widths .5" to 2". Keep in mind that the narrower the logs, the more seams you are dealing with, which translates to a heavier quilt, and all the quilting challenges that go with heavy quilts and lots of seams.
Ok -- I guess photos from the past don't remain on this board. Links:
http://www.flickr.com/photos/12590460@N06/8366545522/
and
http://www.flickr.com/photos/12590460@N06/8365453237/
Both the above have randomized and non-uniform log widths. I just square up the final blocks before assembling.