They can't be compared. The Byakugou is a high level medical ninjutsu, Orochimaru's oral rebirth is a special kawarimi jutsu.
Tho apparently Orochimaru's technique eats up more chakra then the Byakugou.
I'm not really sure if the Ryū no Kawarimi qualifies as a Regeneration Jutsu. It rather seems like a way to 'Respawn', if you will, whereas the Byakugō actually regenerates the users body.
Edit: Eh, on the other hand, the difference is not too vast.In all honesty, they seem to be equally useful, both have their pros and cons. They both grant the user pseudo immortality, and both seem to be quite Chakra taxing [Although the fact does stand that the Byakugō is something one can only use after having actually stored some Chakra for a while] It's pretty hard to pick between the two, but personally I'd go with the Byakugō, seeing as injuries are healed almost instantly, and since it heals only the specific injuries, whereas the Ryū no Kawarimi actually requires you to recreate your entire body, which I'd assume is quite taxing.
well thats a tough choice but orochimarus would be the more convenient justsu seeing as you have to store chakra for a long time in one specific point in order to get the byakugou. it took sakura 3 years to get it and it put tsunade in a coma from using it all and it cant help her from being cut in half as we saw but orochimaru got cut in half and he couldn't seem to care less lol. plus i don't think the byakugou restores limbs so thats a downside cause tsunade without an arm is almost completely useless while orochimaru can just restore it
They're essentially the same, but I would prefer Byakugou, because it's passive, rather than active, so you can't really be taken down by a surprise, unlike Kawarimi.