Either will work. The rule of thumb I use is that if I'm gonna let the database do a fair bit of work on dates (i.e. select * from logs where date > now()-1month kinda stuff) then I usually store them as date stamps.
If I'm gonna do most of the processing in unix (i.e. print date("Y m j",$time) ) then I store them as unix timestamps.
note that Unix time stamps only have a resolution of 1 second, whereas many databases have finer time resolution, so if you need sub second timing, then you need to use the database's date functionality. Also, most databases can store dates well outside the Unix 32 bit epoch (1972 to 2037) so if you were storing dates from outside those ranges, again, the database is the best choice.
Also, many databases can store timestamps with timezone information, so if you need to store dates with timezone info you'll need to let the database do it.