When the 9th Doctor took Time Vortex from Rose just for few seconds, his cells started to die leaving him no choice but to regenerate.
Previously, Rose possessed Time Vortex for several minutes (She spent time in TARDIS while coming to The Doctor from 21st century and then her dialogue time while killing Daleks etc), but she didn't die. Why?
Provided that humans are softer than Time Lords and she possessed Time Vortex for longer duration, why didn't she die?
I believe her conversation afterwards indicates that it's more like she was possessed and the TARDIS kept her safe, as it was her plan to save The Doctor.
We know that the TARDIS is conscious (6x04 The Doctor's Wife), and Rose also seems to indicate this in her line:
I looked into the TARDIS, and the TARDIS looked into me.
Sure, the Doctor corrects her ("You looked into the time vortex. Rose, no-one's meant to see that."), but it may be that The Doctor simply doesn't realise this yet (As until The Doctor's Wife, it had been established that only later model TARDISes were known to be conscious).
With all this in mind, I think it makes her final conversation with The Doctor more meaningful:
Rose: What happened?
The Doctor: Don't you remember?
Rose: It's like. . .there was this singing.
The Doctor: That's right, I sang a song and the Daleks ran away!
Rose: I was at home... No, I wasn't, I was in the Tardis and there was this light. I can't remember anything else.
There are also similarities between the look of the "essence" that The Doctor removed from Rose and blew back into the TARDIS, and the "essence" of the TARDIS escaping from Idris in The Doctor's Wife:
As to why it still caused The Doctor to die, that may be because Time Lords are already operating on a similar plane of consciousness to the TARDIS, as the Doctor hints at:
Rose: I can see everything. All that is, all that was, all that ever could be.
The Doctor: That's what I see, all the time.
Which would make the effect of having another consciousness inhabit their own even more stressful on their physiology than on a human.
I see what happend after reading crow t robots answer I have a better one rose absorbs the time vortex and it binds its self to her and when the doctor takes it it gets confused rejecting the doctors time Lord biology thinking it should be human and starts to kill his time Lord cells not giving the time vortex enough time to realise the change and heal him the doctor puts it back into the tardis leaving himself no choice but to regenerate or it wasn't meant to be transferred from person to person and it got tainted from being in rose a human and that's why it was killing his cells if he was the one to look straight into the heart and then put it back himself I'm sure he would be fine just like rose was and as for saying that's what i see all the time I think he means his travels not literally like rose the 10th doctor says if a time Lord was to absorb the time vortex he'd become a god a vengeful god that's why 9th got rid of it as soon as possible he didn't want the power to overwhelm him so if the seccond consciousness was to stressful on their physiology 10th wouldn't have said a time Lord would become a god or crow t is right but not cause of his physiology but due to him being a time Lord and time Lord's all look into the tempered schism which is a temperd version of the time vortex and the one that is the heart of the tardis is pure unrefined time vortex energy
