Is it better to sell items or to just ship them?

Items put in the shipping container and selling directly to stores will net the same profit, so there is no difference there (Source).

With the shipping container:

• You must wait a day for your money
• Adds to the 'items shipped' statistic in the stats screen
• No concern about when shops are open
• You can put artifacts you cannot sell in the shipping container for some profit (Source)
• There are three achievements for shipping items. One for shipping 1 of every item, one for 15 of every item, and one for shipping 300 of any single item (Source). These exclude artifacts. A full list of items needed for achievements can be found here.

The opposites of these points are true with selling to shops.

Based on these differences, unless you need money the same day, there is no downside to simply using the shipping box.