I absolutely think it's wonderful that my dd has such a close, loving relationship with my MIL. She has sleepovers at her house about once every month or so. Both DD and MIL totally love it. DD hugs us goodbye and then gets busy with her grandmother with no visible upset or discomfort. We call her a few times during the evening and then in the morning, and arrange when we'll come get her or when her grandmother will bring her home. Once she's back with us, she will often cry that she misses her grandmother, and for a few days afterwards, will get sad from time to time and say, "I miss Daddy's Mommy!" She will ask to call her, and we do that as often as she wants. Truly, this is someone she loves to be with, and the time they spend alone together is very very special to both of them.
On the other hand, being alone with my parents is something she doesn't do often. They live out of town, which is most of the reason, but there are some other issues too, and we don't really leave her with them that often. HOWEVER, when they visit us or we visit them, she insists on THEM putting her to sleep at night. We get hugs and kisses goodnight, and then THEY read her stories and sing her songs and tuck her in...all at her request. My parents love this and drag bedtime out as long as they can, which is ok with us for as often as it happens.
I think the key to our happiness with the situation is that DD really is enthusiastic about it, in both cases. The few times we've left her with a neighborhood sitter, she's not even remotely as happy. She'll tell us later that she liked the person, that she had fun, that she wants that person to come back and play, but she cries when we leave. I think the key is, as a previous poster said, that the neighborhood sitter doesn't love DD like her grandparents do. THAT'S the major difference.