On end with four feet sticking up is going to be hard regardless of whether you use a tablesaw or router table.
I’ve never done box joints on anything that wide, but if I was going to try I think I would try doing it on my table saw for the following reasons:
1) Taking 3/4 deep by 3/4 wide box joints is going to be really tough on your router bit. Generally, taking more then 1/8 -1/4 inch per pass is all that’s suggested.
2) I think you will need to use a sled that you can attach your board to so it won’t move when cutting it. To improve the chance of success, I’d try to use both miter tracks that are found on table saws. Router tables rarely have more then one.
3) using a dado blade will allow for very precise adjustments to width of cut to make slight adjustments to your fit. Router bits make fixed size cuts.
There are many videos showing the process of cutting and spacing for the next cut, I’d look for ideas that help dealing with large pieces of wood. Like I say, a sled with solid right angle support tall enough to clamp your board. It might be a pain, clamping and unclamping every cut, but maybe you won’t have too, but if you need to the option exists.
I’d also like to suggest that you cut both long pieces at the same time, saving time and clamping. It also assures that if you screw it up, you can just make your box a little smaller by cutting off the end and starting over. Actually, you should probably cut the first end on oversized boards just to test the fit with actual material. You can resize after first end is successfully cut.
In woodworking there is always more then one way to accomplish something.