Essentially, based on the war in the East, there are two possibilities.
One of them is that Union soldiers were generally worse than Confederate ones, based on the occasions when the Confederates scored well in CEV terms despite being outnumbered (That is, the Confederates did better in terms of casualties inflicted vice taken than we would expect from Lanchester Square) and the times when Confederates on the attack outperformed Union troops on the defensive.
The other option is that the soldiers were broadly comparable, and that it was the quality of the generals which changes things around.
IMO... well, a bit of both. If you ignore McClellan you can make a general claim that "when on the attack the Union got a CEV result of 0.2, and when on the defensive the Union got a CEV of less than one"; that is, the Confederates outperformed CEV by roughly a factor of two both attacking and defending. This would imply that either Lee was a thundercracker of a general to a roughly identical extent over every Union general considered (Pope, Burn, Hooker, Meade, Grant) or that Confederate troops were generally substantially better. (If the two armies were equal then the Union attacking CEV times the Union defending CEV should equal roughly one.)
But once McClellan is included the numbers change. McClellan's offensive CEV times his defensive CEV against Lee is somewhat better than one.
The way to explain this that I think makes sense is:
In the Civil War in the East, the Union troop quality overall went down over time and the Confederate troop quality overall went up over time.
The quality of Confederate generalship remained roughly static throughout (it was always Lee).
The Union generals started well (McClellan), went downhill (Pope, Burn, Hooker) and then came back up but did not reach Lee's quality (Meade, Grant).
This would imply in turn that the best Union army was the one led by McClellan early on, and indeed it is this period when the Union army was outfighting the Confederate in both CEV terms and in casualties inflicted for casualties taken; it's also the period when Lee was caught by surprise the most often. Partly this is because of the higher overall quality of the Union army which McClellan built, but the fact that his immediately following generals did much worse than McClellan (despite having more troops in their army than he did against the same AoNV) indicates McClellan's leadership was also part of it.
The quality of an army is dynamic, not static.
A possible confounding variable might be that the AoNV was depleted over time (it started the Seven Days very large and then went up and down in size but on an overall downwards trend), but CEV allows for that. It would be possible to recalculate CEVs based on the linear law, but I've used the square law here (the fact that almost all Union CEV levels are below one means it's unlikely to ruin the conclusion.)
A fun side fact. McClellan's CEV at Antietam is almost identical to Meade's CEV at Gettysburg (both are about 0.7; this means Lee's CEV was in both cases about 1.4). However, at Antietam the Union army was on the attack; either this is a drastic drop in the quality of the Union army from 1862 to 1863 (where they fight only as well behind walls in 1863 as they do attacking the Sunken Road and Dunker Church in 1862) or the general has something to do with it...