The care home may prefer to take people who are self-funding, but I assumed that you were talking about Social Services making a needs assessment,
@sattwood70 .
If you are self-funding you can actually by-pass the needs assessment by SS, but if you have it done, then SS will offer the same thing irrespective of whether you will be self-funded or not. They try and keep people at home for as long as possible and usually only offer a care home if everything else has failed. They have to offer at least one care home who will accept Local Authority funding.
If you are self-funding, though, you can go to any home that will accept the person with dementia. You cannot just "put them in a home" as the care home will make its own checks and safeguarding, but there is definitely more flexibility.