It looks like a berserker can take normal barbarian daily attack powers, which are primal and so would trigger the berserker's berserker's fury, and many of which cause the berserker to enter a rage.
Is there any reason that a berserker doing this wouldn't benefit from both their rage and their fury?
No, there is no reason that prevents Berserker Fury from stacking with the rage benefits.
Also, note that Berserker Fury is a class feature, while rage is not (it is a power keyword which has its own rules).
However, besides for the specific rage daily power's benefits, there are no rage side-effects that could stack with Berserker Fury. In fact, Berserker Fury modifies basic melee attacks and some Martial Barbarian attack; while Rage affects Primal attacks only.
I think the big change comes from now you can still do your barbarian's damage while you are under the fury but now add a multitude of small affects while removing the small hindering parts.
Example: *Devastating strike at-will [1W] + 1d8 + [STR] effect take a -2 to AC until start of your next turn. The alternative is that while you are under fury you can now choose to either do shift 2 squares before the attack, slow the target after the attack or make the target grant combat advantage without taking a -2 AC unless that's the effect you wanted to go for.
Also if there are any previous rages that cite it does extra damage for primal attacks or anything like that going into the fury grants all the martial powers the keyword of Primal so you'd still have those effects tied to them.
Another thing, looking at the book it does not seem that berserk takes the place of rageblood or thaneborn or any alternatives in Primal powers so you can keep your damage up without taking -2 AC and still rage/get bonuses from feral might.
