I have a 20 year old Navel orange tree in my backyard planted by the previous owner of the house. He told me that the oranges were very sweet and juicy (he let the sprinkler water it).
I have owned this house for over 10 years now and though the oranges are juicy, they are ever sweet like store bought Navels. I removed the sprinklers and am hand watering depending on how dry that area is. I also fertilize with a slow release citrus fertilizer as per instructions on package.
The oranges are palatable enough but makes your face pucker up while eating them. I try to delay the harvest by a few weeks and that makes them sweeten up a little. They are all navel fruit, so I am pretty sure that there is no rootstock taking over and producing weird fruit. We cut off the ornamental trees all around it 4 years ago and it gets full blazing sun for atleast 6 hours even in the winter. It is against the fence, but it is much taller than the fence. My next door neighbor gets sweet navels on her tree, so I am wondering if the issue is related cultural practices. How can I improve the quality of my fruit?

Can you post a picture of the fruit and maybe even the tree? Do the fruit all have THE navel at the bottom on each fruit?Are you fertilizing, when, how often and with what?

All the fruit are navels with the characteristic navel in them. They do taste like navels, but a little unripe. I start fertilizing in March with a slow release fertilizer called Vigoro Citrus and Avocado fertilizer. I apply every three months as per the instructions on the bag. We are having a rainstorm now, so, I will post pictures after I am able to approach the tree to get pics.

We've had a late season here in the Central Valley Citrus areas. I'd wait until May and see if they taste better then. Our Late Navel varieties are harvested April thru June.