I was looking at both last fall, and in the end bought the Corolla, though CE (with Enhanced Convenience Package). The major reason for selecting it was the price - similarly equipped Civic would be much more expensive, and I didn't have the money. Now I wish I would have the Civic. While Corolla is pleasant to drive, quiet and smooth, the seat comfort is terrible. I'm a thin guy (6'2" and 180 pounds), and the seat cushion is too narrow - the side bolsters dig into my butt, making it very uncomfortable on longer drives. Maybe if I had a big, fat-upholstered butt, I wouldn't feel the narrow seat cushion... Unfortunately, this poor seat design didn't show up during the test drive - it took a few weeks of driving to sink in. Also, there is no lumbar support. One big advantage of Corolla over Civic might be the quietness. While commuting to work it probably makes no difference, but on long drives it's nice to have a quiet car, and being able to listen to music, rather than the road noise.
If you're thinking about buying Corolla, check the comfort of the front seats with the understanding that if you feel suspicious pressure on your butt, it would get much worse later on... Amazing that Toyota can't design a comfortable car seat, while even Hyundai can...