The spec for the <matrix> element states that COLLADA matrices are column-major ordered. I would assume that the COMMON fx_basic_type_common float4x4 is the same.
I just wrote a little piece of code comparing values of e.g. domFx_basic_type_common and domGlsl_param_type. After reading this old thread again, I was puzzled about the answer regarding the float4x4 internal format. Because the spec says:
page 93:
Matrices in COLLADA are column matrices in the mathematical sense. These matrices are written in row-
major order to aid the human reader. See the example below.
So in fact the answer about the programmatic matrix format is row-major, not column-major, which is, of course, very important when comparing matrix-values of different profiles.
There is not really any wrong statement in the spec. You just have to be aware of the difference of vector convention, which is column-order, and the actual storage format which is row-major. But if you just quickly skim through this section of the spec you might mistake the column-order vector convention as the memory layout.
Anyway, i opened a bug to emphasize the storage format in the Spec: