In the meetings I attended, there was no doubt that the "higher power" being contemplated was the traditional, theistic, Western God of the Christianity and the Bible. This didn't surprise me much since I was aware of AA's roots in the Oxford Movement. Certainly a first-blush reading of the Big Book would seem to suggest belief in such a God -- with the occasional
"of your understanding" thrown in as a sort of peace offering to non-believers. Often in meetings, I would encounter members who, when quoting passages in the Big Book which contained the
"Higher Power" phrase, felt obliged to offer the emendation,
"whom I choose to call GOD."
I was eventually able to arrive at a God concept of my own understanding which works very well for me as applied to the 12 Steps and is non-theistic, but I can't give much credit for it to the people I encountered in the rooms.
I found much more of a free-thinking, open-minded approach on forums such as (and including) SR.