Since I watch a lot of anime, I end up hearing these two particles a lot, but I've never been completely certain of their distinction, only that there definitely is one. My dictionary listed them as a single entry with the definition of adding emphasis, which seems to fit well with ぞ, but not quite as well with ぜ from my observation. It also doesn't help that as far as I'm aware, almost nobody says these in real life, or at least much less frequently.
Your observation is accurate. There is difference between ぞ and ぜ, though ぜ has almost died out, at least in greater Tokyo. Basically, ぞ just straightforwardly tells one-sided subjective claims, while ぜ has function of confirmation, request, or advice, only in a rude and self-centered manner. ぜ couldn't be used if there's no listener, that is, you wouldn't speak to yourself with ぜ.
The last remaining usage of ぜ occasionally heard around me is an indicator of speaker's annoyance or vexation.
There's no point waiting anymore. Come on, let's go already!
In anime and other works of fiction, ぜ sounds more tomboyish, boyish and/or childish. Typical users of ぜ are male kids from so-called 少年マンガ. For example, Satoshi from Pokémon uses ぜ frequently. An adult male character rarely uses ぜ, while ぞ may be used by old male people (and sometimes even by women who are speaking a bit playfully).
In the real world, ぞ is sometimes used in casual and brusque conversations between adults. ぜ is much rarer, and no one around me uses ぜ actively. Even native speakers can sometimes wonder if there are any real people who use ぜ.