I'm on some heavy duty pain relief so sorry if this is jumbled.
Having work in homes and in home care here's my opinion.
Care Home:
Pro's - There's always someone around.
It's easier to access outside services, (social workers, speech therapy, OT)
Specialised Equipment like hoists, adaptable bed and standing frames.
Cons:
In some homes the care given is to suit the staff not the clients, such as bed time, getting up time, having a cup of tea when the client fancies one.
Language barrier, some homes recruit staff from overseas and don't have a minimum English standard.
As a family, you may need to be constantly asking for changes and speaking to the manager about issues.
Home Care
It may be that she would have a live in carer but with a second carer to join for hoisting and incontinence care. So 8am 2 carers to wash, dress and out of bed, 2 carers for lunch time for continence care, in the afternoon the live in carer would have a couple of hours off with incontinence care before and after. Then 2 carers at bedtime.
Pros: It's her own home, with her own things around her. If there will be live in carers then she will build up a relationship with them. The company I worked at the live in care was 1 week on and 1 week off.
There'll always be someone with her.
If she has a suitable vehicle the carer can take her out.
Cons: She may feel intruded upon, a stranger in her home going through her things.
She may not like the carer.
The 2nd carer may be late or very rushed, so she could be in a soiled incontinence pad for longer than would be ideal.
I hope this helps