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.
2 Answers
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.
これ以上待ってもしょうがないし、もうさっさと行こうぜ。
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.
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So they don't necessarily have a different connotation to them, it's just an issue of the speaker or the nuance? I kind of got the impression that ぜ also had a slight element of "seeking agreement" from the other party, but that may be my misinterpretation. Commented Jan 2, 2016 at 23:43
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Both are frequently (mainly?) used when the speaker is excited, or the speaker wants to convince someone. The semantic difference is small, I think.– narutoCommented Jan 3, 2016 at 2:59