I had two kids overlap in college for one year, both HA privates. The financial aid offers were different between the two schools, the EFCs differed by 15%, although both did acknowledge that two kids in college meant we only had to pay half of what they would have calculated for one. I contacted the one that was offering less and pointed out the disparity; they gave us a very small amount more, and basically said that they do things their way and that's just how it is. There were no athletics involved with that school.
Ultimately, what you're getting now are estimates; they won't do the final aid offer until you've submitted the FAFSA and CSS, next spring.
FAFSA is the same for everyone, but CSS for private schools asks different things from school to school. Some wanted to know value of your house. One wanted to know how many cars, and which was your primary car (do we say the 2004 minivan?). Some asked other things. They have formulas (I was told their "proprietary algorithm," and "Institutional Methodology") that determine aid based on all the information they choose to collect. They also all have different resources.