Raw agave is not sweet. It is processed in a way similar to how high fructose corn syrup is processed. Compared to HFCS agave nectar has less glucose and more fructose. Although the ratio is not fixed it is closer to honey. Since honey is not recommended for diabetics, I would not think agave would be a viable sweetener for diabetics. I’m not surprised you had problems with your sugar, because of the presence of glucose, which is absorbed very quickly.
Some people don’t like stevia, but it’s a much better choice. Another option is erythritol a sugar alcohol that some people find works, especially mixed with stevia. Here’s a recent discussion with some more info.