Well there are a few reasons, one is control, you have to admin them with other people being able to post content so often, so your not only not keeping full control of what is posted but you have to monitor every post also, so it can be a lot more work and not as autopilot.
As I say lacking stats makes it hard to prove what posts are doing with traffic, so its really hard to nail trends down. Makes them hard for our end, auditing them is super hard to do.
And then as I said too branding and loyalty is basically non existent. So you are limited in some cases. I would prefer pages over groups in the long term, I reckon. The stats really hurt trading them, because its hard to know what they really doing for 100%