I've used GroceryIQ for some time now and like the synching between my wife's phone and mine, along with the barcode scanning to add items, shopping cart totals, and the fact that it links with Cellfire to let you add coupons. The app is also "powered by" the Coupons.com website.
I've also used it at locations like Lowe's, Wal*Mart, BestBuy etc. so it's not just good for Groceries.
To me, the calendar is Cozi wasn't a big seller because we already share our Google calendars & I didn't need a grocery widget. But other than that, they both look to do the same thing. Cozi just has a paid ad-free version while GroceryIQ is ad-free with free version. But both seem to be strong, well thought out apps.
Another decent one is OurGroceries. Paid app comes ad-free as well and seems to have pretty much what the other two mentioned have.