For me, I'm mostly convinced of the paleo view. It's by no means the only valid view or the whole view but I'm convinced by numerous anecdotes from people I know personally and elsewhere.

Here's one quote from Anna Karenina which suggests that a similar approach was well known in Tolstoy's time:

    On the day of the races at Krasnoe Selo, Vronsky had come
    earlier than usual to eat beefsteak in the common messroom
    of the regiment.  He had no need to be strict with himself,
    as he had very quickly been brought down to the required
    light weight; but still he had to avoid gaining flesh, and
    so he eschewed farinaceous and sweet dishes