The video files on the bluray disks are stored as MPEG-TS files, if you rip to that they will be exactly as they were on the disk. I'm not familiar with the sofware you're talking about, but I presume when they say they'll save H.264 what they mean is that they will use H.264 to reencode the files to something smaller.
Similarly handbrake is not sofware that is used to rip disks, it is simply an H.264 encoder.
Also, though most blurays are H.264 there are some that are VC-1, both codecs are supported by all players for bluray disks.
As for software, I use DVD Fab, which has a free version capable of ripping blurays perfectly fine. I do reencode them with handbrake for space concerns (i've done an A/B between origional files and reencodes and for the life of me cannot pick them out at ~8 GB a film). Both of these are available for mac.