Hopper can't drain from/funnel into the other side of the large chest.
The hopper will only take items out of the container it is directly attached to, making it useless when trying to use it with large chests, requiring a second hopper to drain into the first one. It should recognize the large chest as one container. It also can't pull items out of a large chest, although there's a way around this using a second hopper. No such option exists with to pull items out of a storage minecart and into a large chest however, making this bug very frustrating.