It always depends on the games/roms whenever this question is brought up.
if its 512 MB, you can fit about 512 MB worth of roms, make sense?
Thats why I dont like the "holds up to 6468435156468 songs" when they talk about Mp3 players. I bet I could fit more than that with a lower bitrate or shorter songs.
So to sum it up, it all depends on the size of the games you want to put on there. Check the Releases section of gbatemp to find out the sizes of the games and do the math to see if what you want on there will fit....
EDIT: by the way, more on topic, it uses microSD cards for storing the roms.
EZ-FLASH 4 Lite Deluxe features:
256Mb PSRAM (32 Mbytes)
384Mb NorFLASH (48Mbytes)
32Mb Loader (4 Mbytes)
8Mb saver SRAM (1Mbyte)
that might be the onboard memory you heard/read about.