Ride hight is different
I have a 3AJ Tenere (twin headlight fairing) and my wife has a XT600E which we did a 2 year trip through Asia and Australia on, so I feel well placed comment on their differences.
Before we changed the old rear shocks the Tenere was much taller than the 600E. I fitted the same aftermarket rear shock and fork springs and the Tenere seat hight is still much taller.
All Xt600 have reliability issues with 5th gear, but after 1996 (I think) it was greatly improved.
Tener air filter can be serviced on the road as it is an oiled foam type. 600E air filter is disposable paper filter, an alternative is needed for a big trip.
Terere has 18 inch rear wheel, 600E has 17 inch, this effects tyre choice.
Petrol tank size has already been mentioned, I am happy with the Achabis 23L tank that I fitted to the 600E, but it is an extra cost, and is plastic so limits tank bag choice (as does its shape)
Tenere has a proper engine bash plate, need to buy an aftermarket one for the 600E.
Tenere has CDI ignition and so can run the engine with a dead battery (especially if you have retro-fitted the kick start), 600E has TCI and needs a good battery.
Tenere has a fairing with a wind shield which makes riding less tiring, a handlebar mounted screen can be added to a 600E but they can catch the wind and cause it to weave, especially on part worn tyres. This doesn't happen to my Tenere.
But if you were to ask me which to choose for a big trip through the developing world I would suggest that if you are over 6 foot the 600E might be a bit cramped, if you are over 6 foot the tenere might be too tall for you to get your feet down, but ultimately it will depend on what you can find for sale in decent condition.