I have wanted to address this for a while, Mitch. Not sure why I haven’t yet.
It doesn’t really matter if a coach or a coordinator wants to run a 4-3 defense or a 3-4 defense, or 2-3-5, 5-2, 3-1-6 or something else for that matter. Every team runs some sort of hybrid defense, so at least schematically it’s not a problem to fit almost every player into the system. I think the main reason we are talking about it in that static way could be as simple as how the networks must present some lineups, and it is simply easier to set it up in either a 3-4- or a 4-3-lineup.
The important part is if the coach wants to run zone- or man coverage, what blitz packages he likes, if he plays one-gap or two-gap on the defensive line, and other dynamic stuff like that. For example, that is also the difference between, say, Todd Bowles and Ray Horton even though both of them runs a 3-4 base defense.