Is varchar(x) as fast as `text CHECK ( char_length(x) )`?
No, it's not strictly true. Here is what the linked docs say,


  There is no performance difference among these three types, apart from increased storage space when using the blank-padded type, and a few extra CPU cycles to check the length when storing into a length-constrained column. While character(n) has performance advantages in some other database systems, there is no such advantage in PostgreSQL; in fact character(n) is usually the slowest of the three because of its additional storage costs. In most situations text or character varying should be used instead.


So essentially


There is no reason to use varchar over text when the column is unconstrained. This is not true in some databases, namely ones that implement schemes like VARCHAR(max).
When it's constrained in a column, it's slower. There is a reason to use varchar(x) over text CHECK ( length(x) &lt;= x)


Example

You can easily see this,

\timing 1

CREATE TABLE foo (
  x varchar(255) NOT NULL
);

CREATE TABLE bar (
  x text NOT NULL 
    CHECK (char_length(x) &lt;= 255)
);

INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);

INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);

INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);

INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);


Note, char_length and length are the same here. They internally call textlen.

Results

test=# INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
Time: 1156.529 ms
test=# INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);
Time: 1268.869 ms
test=# INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
Time: 1107.869 ms
test=# INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);
Time: 1283.043 ms
test=# INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
Time: 1121.788 ms
test=# INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);
Time: 1238.194 ms
test=# INSERT INTO foo SELECT 'x' FROM generate_series(1,1e6);
Time: 1116.421 ms
test=# INSERT INTO bar SELECT 'x' FROM generate_series(1,1e6);
Time: 1248.272 ms


In each case, the insert into bar is slower

Type-constraints rechecked

I would have though too that the checks would have carried over to tables using the same types. This kind of optimization may be possible some day, but alas no joy,

test=# CREATE TABLE foo2 ( LIKE foo INCLUDING ALL );
Time: 7.143 ms
test=# CREATE TABLE bar2 ( LIKE bar INCLUDING ALL );
CREATE TABLE
Time: 10.762 ms
test=# INSERT INTO foo2 TABLE foo;
Time: 3613.517 ms
test=# INSERT INTO bar2 TABLE bar;
Time: 4061.650 ms


Though the varchar form is still noticeably faster.

Other Notes

As it relates to emails the subject of the tweet, this post may also be useful.