What's mysql's "BETWEEN" performance over..?

As I recall, there's no difference. But see for yourself if:

explain plan for 
SELECT * FROM `table` WHERE `unix_date` BETWEEN 1291736700 AND 1291737300

and:

explain plan for
SELECT * FROM `table` WHERE `unix_date` >= 1291736700 AND `unix_date` <= 1291737300

produce the same plans.

From the documentation:

• expr BETWEEN min AND max

If expr is greater than or equal to min and expr is less than or equal to max, BETWEEN returns 1, otherwise it returns 0. This is equivalent to the expression (min <= expr AND expr <= max) if all the arguments are of the same type. Otherwise type conversion takes place according to the rules described in Section 11.2, “Type Conversion in Expression Evaluation”, but applied to all the three arguments.

So it really is just syntax sugar.