I don't have young children around to more closely interact with my pet birds. When they do come over and show curiosity towards the birds, I give them a quick tour and explain to them the right way to approach the cage and how to correctly address the bird in question. It's vital to educate children prior to letting them handle the bird.
Lovebirds have a sturdier build when compared to budgies and also have bigger beaks that are able to do more damage.
The temperament and personality of a bird is a very important aspect and this can determine if said bird is to be allowed around small children or not, the proper socialization is also vital.
This applies for both lovebirds and budgies. While budgies have small beaks, their bites can also break through the skin.