I'm not sure. I have a cynical view about NHS Continuing Healthcare - I call it the freebie with strings, after my mother with Parkinson's was placed on it back in March 2014. Afterwards, we couldn't get the Surrey care home to give her drink, they were funny about it, and it took a while to twig what it meant. She died in October 2017, but my sister and I had to spend the interim visiting the care home to give her drink because each successive Surrey care home seemed mysteriously unable to.
To clarify what I mean, Google 'NICE end of life guidelines' and you might be quicker on the uptake than I was.
That said, if your parent is terminal then there's no arguing with it, but - and I am very sorry to say this - I am not entirely sure that if they are offering something free they won't feel they are morally entitled to approve the end date. That can be better carried out in a nursing home setting.
I would make it very clear what you are expecting and what you are getting in to. If your parent is cogent, get her wishes recorded and on the record, and written down and emailed to the authorities concerned.
Pros at home: You have control. You set the pace. You don't have to deal with chilly nightmare care home managers where it's implicit that your parent's death just may be saving someone money. You don't have to deal with shouting dementia riddled nutters or unhinged carers.
At home, you can probably take your parent out at any time, and if your home looks good and is in a nice area with a park and coffee shop, great.
At home, you can give your parent drink at any time.
You are less likely to be in a power struggle.
But, you don't get away from the situation, and your parent doesn't get to mix with so many people to distract from her own situation. Sometimes meeting other residents and relatives can be enjoyable. So choose a care home with a lot of traffic, people coming and going.
Unfortunately, it's hard to assess care homes because of the paucity of care home review websites, most of which are rigged, and the dodgy CQC which sits on damning care home inspections for months at a time.
Your situation is different to mine, as my mother had Parkinson's... I don't know about getting NHS Cont Healthcare at home, it may be possible. You don't mention what sort of level of care we're talking about, in terms of hoisting and so on. I should come clean and say a lot of tension between us and the care homes was down to a) My whistleblowing a care home that had nearly killed my mother earlier (no one held repsonsible, natch) and b) That I'd clearly rumbled something odd was going on with my mother's hydration - that later care homes were covertly killing her basically - and they were scared I'd whistleblow again. (Not scared enough to give her a fucking drink, though.)