I worked for three years in centre care. The big difference I would notice would be one teacher that the child learns to know and love at a dayhome. In the centre I worked in there was lots of comings and goings of the ECE's. Also the children only saw the four walls of the centre and the four fences of their playground. Most home daycares attend parks and go for a walk and some even do field trips :-) Children learn so much from the world around them and they have the next 20 years to be institutionalized in a school setting.
I also find home care to be a little more forgiving in their sick policy. The centre I worked at sent kids home so often for the littlest thing (ex. one diarrhea and home for a minimum of 24 hours of diarrhea free) even in a 12 month old!!!! How did some of these parents keep their jobs was beyond me. Some did leave for home care but the centre had a huge wait list so it didn't matter to them.
It was great for me in the way that I didn't have to deal with any difficult conversations with the parents. But I also didn't get to celebrate in anything positive or even talk about their child's day as my shift ended at 4:15 and most parents picked up after 5!
Both have their pros and cons but I do prefer home care for myself and my own children (at the centre I brought my child to work with me) although I did enjoy being off at 4:15 back then