I think as many have said there's more potential for things to go wrong.
If a nanny's own child is around then parenting style differences become even more pronounced. As a nanny so far I've been happy to bite my tongue and do it the parent's way, if I went back to work with my own child I'd be a lot less happy about that.
A lot of nannies won't accept the paycut which employers resent. Now in my view a drop in pay of £1/hour is childcare for £1/hour for the nanny. It's no longer one-one care, it's shared with an extra child and you wouldn't pay the full rate for a nannyshare, would you?
Some employers feel that the nanny will put their own child first and to be fair some nannies will.
It introduces logistical issues after a couple of years unless nanny's child is going to the same nursery for the same sessions/the same school.
You need extra stuff, you're accomodating an extra child - who pays for a double buggy if one is needed? Who pays for nanny's child to attend activities? What if nanny wouldn't choose that activity for their own child but you want yours to do it?
It limits the range of activities on offer in some cases e.g. swimming.
The fundamental difference is that peopel either have a nanny for convenience or because they want an element of control that they don't have over a SE CM in terms of sole care for their child or someone who will follow their wishes re: routine/food/activities. Someone who used to use a CM, is used to that set up and can get a nanny with own child for the same cost is going to be much more amenable to the arrangement (as long as their experience with shared care at a CM's was positive) than someone who is having a nanny because they want undivided attention and a greater measure of control. And some employers fall between the two - they need a nanny for convenience sake, wouldn't want to be at the mercy of a CM's t&cs but have nothing against shared care.
It's a very complex balancing act and quite often people don't think about the potential downsides, so it smacks them in the face when things go wrong.