Here is the info on the coupons:
"JoAnn will take coupons from Michaels, Hancock Fabrics, and Hobby Lobby. They also let you use more than coupon per purchase. So if you have a 40% off any 1 regular-priced item coupon from Michaels, Hancock, and Hobby Lobby, you can use all 3 if you are buying at least 3 items. The one major exclusion is that JoAnn will NOT accept a competitor’s coupon good for an item they don’t carry. For example, you can’t use a Michaels coupon when buying fabric at JoAnn’s since Michaels doesn’t sell fabric.
Michaels will happily accept competitor coupons from the following retailers: AC Moore, JoAnn Fabric and Crafts, Ben Franklin, and Hobby Lobby. The cool thing about Michaels is they’ll let you use more than one coupon per transaction. So for example, if you have a Joann coupon good for 40% off any 1 item, you can use it with a Michaels printable coupon good for 25% off your entire purchase. Keep in mind that the item you got for 40% off will be not be eligible for the 25% discount as well.
It is also worth noting that Michaels will not accept competitor coupons good for a flat percentage off your entire order. They won’t take a 25% off your entire order coupon from Ben Franklin but they’ll happily accept a 50% off any 1 item coupon." - Kyle, a blogger at Rather-be-shopping.com.
Hobby Lobby is a lot simpler. They will not take competitor coupons, but their 40% one regular priced item is literally available on their website 24/7, while JoAnn and Michaels will change periodically.
Note that Hobby Lobby will only accept one coupon per day.
Diane B. is right about what each store carries.
Joann is more focused on fabric/sewing, Michaels is more focused on straight crafts, and Hobby Lobby is more generalized. So if you're looking for the best selection of thread, JoAnn. If you're looking for the best selection of home accents or furniture, Hobby Lobby. If you're looking for the best selection of spray paint, Michaels. And it goes on.
Hope this clarifies the coupons a bit.