A Decisive Fight Between D-life and L-life

Here's an idea I was unable to give away even to a publication that usually accepts material for free, the Journal of Irreproducible Results. It went like this: precisely two living things, one D-amino-acid-based and the other L-, sprang up simultaneously and side by side, they immediately came to blows, L won, and the rest is, as they ought to say but don't, pre-history. The last I checked, which was the research for this, no one had yet figured out why all living things are made with L-amino acids. And who can? This is, as I say, pre-history: nothing was observed, nothing was recorded, nothing is verifiable, nothing is disprovable. Which puts origins-of-life instantly and firmly in the company of creationism, climatology, and political science. You frame the problem and you hazard a solution, and if it's unpersuasive, you reframe the problem. You can't lose!

Anyway, still running with the idea of a microscopic fight, I've tried to imagine how such combat would be effected. These single D- and L-based organisms burgeoning in close quarters: would they be competing? Not for amino acids, if they're in a stew of D- and L-amino acids and those useful to one are meaningless to the other. The possibilities for one organism giving offense to the other are numerous. I suppose one guy might develop the ability to isomerize the other guy's chiral meal tickets - that'd put him on a diet right quick. But far more simply: might they both compete for an achiral nutrient? Might both need light, or proximity to some source of energy or sustenance, and one just blocks the other? If these organisms are less than three-dimensional, would that make a difference?

Since ain't no tongue ever gonna tell for sure, I will essay the easiest thing, which asks only that one specify (imagine) the following:

The number of dimensions each organism possesses (since they are postulated to have arisen at the same time and place, and be mirror images, assume the same for both)
The number of dimensions each organism LIVES IN (do NOT assume these are the same! The two may be butted against each other, one lives in a hole and the other doesn't, one's moving and the other's stationary, etc.)
The number of dimensions of the interface between the organisms

An organism is considered to have the advantage over its rival if

it's got all its rival's dimensions covered, and
it lives in more dimensions than its rival

For example, if the two organisms are flat, and one lies on top of the other, I'd say the one above is the one ahead. The fill-ins below are preset to reflect this particular situation, but feel free to change 'em around.