I never took one yet. I have only played 4 games of E:A yet, having recently switched from Netepic. So most of the armies in our group were pretty conservative, so that we didn't encounter any problems with activation difference yet.
In Netepic, however, you have a similar problem, the difference in activations is even worse. We tried some different approaches to cope with it. The following worked really well, at least for us:
1) At the beginning of each turn, count your total activations (on- AND off-board). The difference between the 2 Activation counts has to be activated as soon as possible.
2) Roll for initiative. The winner chooses whether he wants to go first or not as normal.
Example:
3k points battle
1st turn:
Eldar activations: 12 (2 are offboard)
Marine activations: 10 (4 are offboard)
Marines win the initiative and choose to go first.
The difference between the activations is "two", so the marine player has to activate 2 formations in his first go.
Note that it doesn't matter whether formations are offboard or not, so that you cannot tinker with this.
2nd turn:
marines have killed 4 eldar formations.
Eldar activations: 8
Marine activations: 10
Eldar win the initiative and go first
The Eldar activate one unit, after which the Marine player activates 2 units. After that players again alternate one activation after another as usual.
It's actually not as clumsy and complicated as my attempt to describe it

.
I would be interested to hear feedback, should anyone want to try this out, too.
cheers
sanjuro