The really important thing is that you gain the knowledge so you can handle the technical aspects needed for various production methods.
How you gain that knowledge is often of little consequence. Whether it's from a certificate program, an Associates Degree, or on-the-job training doesn't matter after you land that first (decent) job in the profession.
A formal education merely gives perspective employers some indication that you should have at least touched upon technical aspects you will need. Previous employment positions on the same career track do essentially the same thing. So really it all boils down to what you learn, not necessarily the piece of paper you receive, if any, for learning.
On the whole, neither a certificate or associates program is inherently better. Although on paper, due to existing competition, often more schooling looks more favorably if you have zero work experience. This is easily offset by any actual work experience though. A new designer with a certificate and six months of work experience and a fantastic portfolio can easily offset a new designer with an Associates degree and zero work experience and a so-so portfolio.
You need to dig a bit deeper to see what each educational track covers. You should be more interested in "lab" or "study" time as opposed to "lecture" time. You'll want hands-on experience, not "listen to this" experience. Which program do you feel will result in a better portfolio in the area you want to gravitate to? Does the certificate program cover more web design than print design? Is the associate's track geared more towards traditional production methods or digital methods? That sort of thing.
No one can really state emphatically that one is better than the other without knowing in detail what is covered in each.