In general, legislation requires the staff of commercial daycare centers to have some training in early childhood education. In-home providers may not have as much training; however, your caregiver appears well-qualified.
You certainly shouldn't move your son to a commercial center because they have computers and a wider curriculum. People who push computers and structured learning activities for young children simply don't understand that it is play that teaches kids the important things they need to know. This is how they discover that wood floats and coins sink as they play with these objects in a tub of water.
Your son has an ample number of playmates his age in the in-home setting. There are few advantages to putting him in contact with more children. At his age, children often prefer to play by themselves or with just one child. Also, he is less likely to pick up illnesses with a smaller number of children.
In-home care is giving your child the chance to bond with just one caregiver. If you put him in a daycare center, he will have more than one caregiver. There's also a good chance that he'll have many caregivers, because centers have a very high staff turnover rate.
If your child is happy, then there are no real gains to uprooting him. When he is three and a half or four, you might want to consider enrolling him part-time in a preschool to smooth the transition to kindergarten.