My husband was stationed at NAS Jax several years ago. He now lives in DC. We decided to stay here because of the housing market and the commute.
Personally, we are very happy over here on this side of the bridge. The roads through Orange Park/Fleming Island seem to be (to us, at least) much worse than San Jose Blvd. Once you get on 295, the traffic usually flows pretty freely and if you lived over here, he would be going against the traffic.
St. Johns County schools are ranked the best in the state.
But PLEASE, don't rule out DUVAL if your husband is in the military. I think you said your kids are young, but Duval does have a great magnet school system and it's AUTOMATIC entry if you move into the county while on Active Duty. This is especially important if your kids are in middle/high school. Paxon and Stanton Prep are two of the best in the nation. Even if this doesn't apply to you, pass the word. I think it's important for military families to know the benefits that they have when moving to different duty stations.
As far as shopping goes, you heard right from the PPs. No Aldi's, no double coupons and Costco about 30 mins. away. LOVE the St. Johns Town Center. Hey, and if you are FL residents, no income tax AND you can get the monthly payment plan for your APs!