Arrays instead of join tables

I've never worked with a database with arrays, so I'm curious what the
advantages and disadvantages of using it are. For example:

-- METHOD 1: The "usual" way --

Items table:
item_id int,
item_data1 ...,
item_data2 ...
Primary Key = item_id

ItemSet table: <-- Join table
item_id int,
set_id int
Primary Key = (item_id,set_id)
Foreign Key set_id --> Sets(set_id)
Foreign Key item_id --> Items(item_id)

Sets table:
set_id int,
set_data1 ...,
set_data2 ...
Primary Key = set_id

ItemSet is the table joining Items to Sets in a one-to-many
relationship. The above is how I would typically set that up in a dbms.
But with postgres, I could do this:

-- METHOD 2: Using arrays --

Items table:
item_id int,
set_ids int[], <-- Hey, neato!
item_data1 ...,
item_data2 ...,
Primary Key = item_id

This way I don't even need an ItemSet join table.

+ Efficiency: To return the set_ids for an Item, I could return an array
back to my C# code instead of a bunch of rows with integers. That's
probably faster, right?

- Can't store any additional join info in the ItemSet table, but that's
okay for my application.

? Can I write a constraint to ensure that set_ids has at least one element?

Is this better or worse? Can I enforce referential integrity on the
elements of the set_ids array? Is it more or less efficient? What else
have I missed?