Just because you bring more men into the region, it doesn't mean you get to deploy more men onto the front line. In open terrain, the commander with the higher strategic rating gets to have an advantage in that department.
Also the commanders attached with units factor in their offensive/defensive skills and here Longstreet has a huge advantage over every attacking commander in the field.
You might want to read here: http://www.ageod-forum.com/viewtopic.php?p=129422#p129422
Let me just quote this part:
In open terrain only (clear/prairie/desert/wood), the Units Quotas are modified by leader (rank)*(offensive/defensive rating) depending whether in offensive or defensive posture:
Combat Units Quota: (+25 points)*(rank)*(off/def rating)
Support Units Quota: (+10 points)*(rank)*(off/def rating)
This bonus can be HUGE. A mediocre 1* general with 1 off/def would get a +25 bonus, while a 2* general with a 3 off/def would get a +150 bonus (+60 for support units), so he could bring about 60% more infantry elements to the fight, and twice as much artillery!
Making an educated guess from an admittedly brief look on the pictures, I image the battlefield like that: the union had a much shorter battleline, while their reserves being bottled up in the lines of communication. Still the Union men got to attack onto well dug-in Confederate elite troops. After getting shot down, the next unit gets pulled from the reserves and takes their place. Just to get shot down. And so on.
Fredericksburg springs to mind here.
Also, it seems from the pictures, that you move with two stacks into the battlefield. That is a bad idea if they are not corps of the same army, because they don't necessarily support each other in battle.