The 4800 is a bit smaller front to back, compared to the 3800, but is a fair bit wider (side to side), and also deeper (top to bottom). You can actually stack three levels of racks inside, although the wheel indentations limit you to two levels near the left edge. I can fit 17 racks of 43mm Royals (which are both longer and higher than racks of 39mm chips) inside the 4800 (5 racks x 3 high, 2 racks x 2 high), but that leaves almost no padding around the edges (not suitable if subject to impact), and it is super heavy. You should be able to fit 12 racks of 39mm, all of your plaques, and still have room for cards, buttons, etc. BUT!... find out the inside dimensions and do a test layout (or buy one, remove the padding, set everything inside, and if it doesn't work, then return it for a refund).
The 3800 is a bit of a tight squeeze for me to fit to fit 11 racks of 39mm chips with a bit of padding, definitely not enough room to include plaques, cards and buttons.