Simba's childhood cannot be looked as one piece. It really is two parts: the first being before Mufasa's death, and the second one after.
Before Mufasa's death: Simba is a cocky and very arrogant... little prick.

Okay, somewhat. He loves to break the rules, and if he's not breaking them, he's pushing the edges. Doing anything to make himself look more 'kingly'. It also doesn't help that he probably is forced to spend more time with Zazu than with Mufasa or Sarabi. So while his parents might be much more lacking than say, Nala, Simba still gets along well with them, and is by no means in a bad relationship with his parents, or anyone else in the Pride Lands for that matter. So while he is quick to get on people's nerves, Simba has a good life, if only what he describes as a little boring.
After Mufasa's death: Not only is Simba run off away from home, being blamed for the responsibility of Mufasa's death really took its toll on Simba's moral. Living with Timon and Pumbaa probably helped him a lot more than anyone else who might have found him, because Simba didn't want to talk about his past, and they didn't really want to listen (well, Timon at least). Plus, the Hakuna Matata lifestyle is probably the best short-term solution that Simba could have asked for. Sure, he would eventually need to grow up and face his past, but until then, it might be best for him to ignore it until he is ready. So by no means was Simba's childhood good at this point, is was rather bad I would assume, but living with Timon and Pumbaa made it at least... livable.