I wouldn't compare either the Zodiac or Anima weapons to a zanpaku-to. They both have some elements of one, but lots of fiction has sentient / ensouled weapons.
What makes a zanpaku-to unique is that they all start out with the base form known as an asauchi. This is actually their most powerful state, since they have limitless potential. However, each Soul Reaper that goes to the academy is given an asauchi that, through repeated use, they imprint their soul on, defining its form and abilities. A Soul Reaper's zanpaku-to is thus a reflection of their soul.
A Zodiac Zeta is somewhat similar, but less specified to the user. It's a weapon that is already defined by its vessel and, aside from presumable ease of use, does nothing to enhance its wielder's abilities. Zanpaku-to generally grant their user some superpower or have a unique effect that enhances their wielder's combat ability, given the weapon in question is literally a part / reflection of themselves. A Zeta, by comparison, is rather blasé, being little more than an easily-wielded weapon that glows. (Given this isn't an action game, we can't gauge how useful they actually are beyond stats... which were impressive for when they were released.)
I'd actually say the Anima Weapon is closer to the zanpaku-to than a Zeta, though for shaky reasons. Like zanpaku-to spirits, the spirit of the Anima Weapon has yet to appear to anyone other than us, suggesting it may be unable to do so (Ardashir chalks it up to the spirit being shy, but...). There's also dialogue about how our wielding it is imprinting our soul onto it, rather like the asauchi processing. However our weapons already had defined forms limiting their abilities (the base Antiquated weapon), and again, given this isn't an action game we won't ever know if they grant us any kind of special powers. Unlike a zanpaku-to, Anima weapons are implied to possess sapience - that is, the ability to think and reason for themselves - while zanpaku-to spirits typically only say things their owners already know but don't want to admit (making them kind of like a psychological shadow archetype, but that's a different story).
I've not read or watched Soul Eater; the only shounen I still read is Bleach, and only for closure. As such I'm not in much of a position to make a comparison.
... enough rambling about sentient weapons for 'ya?