So is it best to grow plants almost "TOUCHING" I've seen TONS of gardens that look like they are super full and all overflowing onto each other and I've seen other's where there is a couple incehs between each plant / limbs / leavs and it looks more 'airy'.
Which is better and why?
Since the Earthbox plant spacing is mostly pre-defined, I will assume that you're asking about a more traditional "in the ground" garden scenario. So, here's my opinion as it relates to that.
Sometimes, the spacing of the plants doesn't really matter at all... and, sometimes, it can make a real difference.
In general, if your garden tends to be damp/wet most of the time, a little more spacing for the plants to "get some air" can help ward off disease/rot problems.
For gardens that tend to be too dry, plants being closer together can shade the soil, which often helps to retain some moisture and "choke out" weeds. Wide Row plantings are a popular technique.
That's a very general way to look at it, but lots of other factors can be involved.
Tomato plants seem to like to "rub elbows" with each other.
"Heavy feeders" (like Corn) that take up a lot of nutrients and water, can suffer from lower productivity if spaced too tightly.
For melons, you will think you gave them too much room when planted, and then they look so thick that you can't even find the ground when the vines mature.
Every soil and climate combination is different; so, it's best to just experiment and see what works the best for you.