I have not made a log cabin but I helped my daughter to make one when she was ten. I like the look of the narrower strips better. She used the the method where you cut your first piece (for the center) and then sew it onto a long strip for the second piece and then cut the second piece to length. When she was all finished some of the blocks were as much as 1/2 to 3/4 inch bigger than the others.
So based on that experience I would recommend the following:
1. Measure each block as you finish to ensure that it is the correct size.
2. Double check the seam allowance as you sew (this plays into Step 1.)
3. I would probably cut the strips to the needed log length.