It all depends on what you're looking for. If you're looking for set hours, predictable schedules and a steady work week, an Eikaiwa would in fact be your best bet. Although ALT and other non-Eikaiwa positions can provide the same benefits, the nature of the Eikaiwa makes sudden and unavoidable changes much less probable. I'm sure the position you originally had seemed like quite a sure thing at first. At an Eikaiwa, you'd be less likely to suddenly end up in the same jam all over again with a wild schedule and lack of incentive.
One more small incentive at an Eikaiwa is that it's a business, so there is room for advancement. In a regular ALT teaching position I'm not familiar with any formal advancement structure, I think you're just a teacher living from contract to contract. Maybe someone can chime in and correct me here.
Lastly you can build a repetoir of private students and work for yourself, I know some teachers who had enough private students to go part time, and one who made their entire living off it. Usually though, it takes time in the schools and Eikaiwas to build rapport with individuals who like YOU, your style and methodology, and would follow YOU anywhere you went.
That being said, Eikaiwas do have their obvious drawbacks which have been discussed quite in depth here in various other threads. Most teaching purists scoff at them, so professionally speaking an Eikaiwa may not be for you if you're looking to really reach out and touch someone. Overall the options for English teachers in Japan aren't very numerous and the choices are fairly straight forward. I'd think about how long you really expect to stay in Japan first, remember a job is ultimately a means to an end, do whatever best furthers your goals.