Is there an advantage to moving to 'real' date partitions on MySQL 5.5?
Using to_days to Partition
The to_days function yields a 6 digit number in the 700,000's (in the MEDUIMINT range).
Using DATE or DATETIME to Partition
DATE takes up 3 bytes. DATETIME takes up 8 bytes.
Conjecture
UNIX_TIMESTAMP of today's date exceeds 1.37 billion. It takes 4 bytes to store that. Range partitioning allows for range values that high. Here is an example of that from the MySQL Documentation:

It is also possible to partition a table by RANGE, based on the value
of a TIMESTAMP column, using the UNIX_TIMESTAMP() function, as shown
in this example:
CREATE TABLE quarterly_report_status (
    report_id INT NOT NULL,
    report_status VARCHAR(20) NOT NULL,
    report_updated TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP
)
PARTITION BY RANGE ( UNIX_TIMESTAMP(report_updated) ) (
    PARTITION p0 VALUES LESS THAN ( UNIX_TIMESTAMP('2008-01-01 00:00:00') ),
    PARTITION p1 VALUES LESS THAN ( UNIX_TIMESTAMP('2008-04-01 00:00:00') ),
    PARTITION p2 VALUES LESS THAN ( UNIX_TIMESTAMP('2008-07-01 00:00:00') ),
    PARTITION p3 VALUES LESS THAN ( UNIX_TIMESTAMP('2008-10-01 00:00:00') ),
    PARTITION p4 VALUES LESS THAN ( UNIX_TIMESTAMP('2009-01-01 00:00:00') ),
    PARTITION p5 VALUES LESS THAN ( UNIX_TIMESTAMP('2009-04-01 00:00:00') ),
    PARTITION p6 VALUES LESS THAN ( UNIX_TIMESTAMP('2009-07-01 00:00:00') ),
    PARTITION p7 VALUES LESS THAN ( UNIX_TIMESTAMP('2009-10-01 00:00:00') ),
    PARTITION p8 VALUES LESS THAN ( UNIX_TIMESTAMP('2010-01-01 00:00:00') ),
    PARTITION p9 VALUES LESS THAN (MAXVALUE)
);


Partitions seem to be numerically represented as a 4-byte unsigned integer. As mentioned, DATE takes up 3 bytes, but, from what I have observed, partitions are bounded by 4-byte numbers. Given this, expressing a DATE as a RANGE parameter really does not buy you anything except cleaner syntax for defining the range.
Expressing to_days of a DATE yourself or having mysql do it for you boils down to personal choice.