Aunts and uncles are the same generation as the parents for one thing. For another they often have kids in the same general age range as the parents. If they don't have kids they are not necessarily apt to indulge their brother's or sister's kids. Some may not even like kids, and find them to be annoying.
Grandparents often miss the experience of having little ones around since it may be twenty or more years since they had any around. Plus it is often considered "fun" to indulge the little ones, and not have to deal with the parts that are not fun. (Yes, I know some g-parents raise their grandkids, but they don't tend to be indulgent then. So, it is partially a nostalgic thing and partially because they can often cherry pick the funs things you can do for and with kids.
I am not personally familiar with this paradigm as neither my husband or I were indulged in this way; nor are our parents indulgent with our son, so standard disclaimers apply.