Where boarding tends to work well
A good boarding facility with veterinary staff or a working relationship with a local vet is genuinely well suited to a pet with a more complex or higher-risk condition, since help is immediately on site rather than a phone call away. It also removes any dependence on one person's schedule.
Where a sitter tends to work better
A pet who's anxious in unfamiliar environments, or whose condition benefits from staying in a familiar routine and space, is usually better served at home with a sitter. Less environmental disruption can matter as much as the medical care itself, particularly for stress-sensitive conditions.
The variable that actually matters most
Complexity of the routine, more than the pet's general temperament, is often the deciding factor. A single daily tablet suits either option comfortably. Multiple precisely-timed doses, or anything requiring judgement calls, leans toward whichever option has more reliable oversight for that specific situation.
Whichever you choose, the handover is the same problem
Both a boarding facility and a sitter need the exact same information, current medications, doses, vet contacts, and what's normal for this specific pet, covered in full in everything a cat sitter needs to know. Halo's Carer's Pack works identically for either option.