1) Quality of product (stitching/leather/zips/clasp)
I think they are about the same. Although I tend to think that Chanel workmanship is better. Or is it because its purses are generally more expensive than those of Celine's?
2) Durability of leather
Celine wins! My mom uses my blossom Celine purse (made of goat skin) all the time and throws it on the sofa when she gets home, yet it is still in excellent condition after 2 years. On the other hand, I have to use my lambskin Chanel classic flap and tassel bag very carefully - store them in their boxes after use, stuff tissue inside to maintain their shape, put desiccant inside to absorb moisture etc. In other words, I have to take care of my Chanel purses.
3) Versatility in usage
I agree with Papertiger that Celine looks more formal than Chanel.
4) Outlook and image
Everyone knows a Chanel purse when they see one. Not everyone knows a Celine purse when they see one. Sometimes I like the feeling of carrying a designer bag which no one has seen before. You will be walking on the road and sense someone eye-ing you and your purse. Maybe they will come up to you and compliment you, "wow, that's a beautiful bag, where did you get it from?" That's the feeling I have with my Celine collection - a thrill of carrying the ONE and the ONLY mysterious gem that others don't. This exclusiveness seldom applies to Chanel, unless you are talking about limited editions. Still, people can tell the CC logo from afar. The excitement for novelty is simply not there. Don't get me wrong, I absolutely adore Chanel, especially on days when I want to show them off. To me, that's the key difference between Chanel and Celine.