This is the kinda debate that is very very personal choice. My Wife and I did UK to South Africa (west coast) then South east Asia to Australia 2-up on a 2000 Africa Twin (750cc). The bike and we were fine, there were a few very tricky spots where MrsX had to walk for 50m or so but other then that it was do able. MrsX has her license so for us it was totally choice.

There are lots of pros/con for two up and two bike (one up), others have covered most of them so i wont rehash.
others:
Parking has to be twice as big for 2 bike. (we squeezed in to very small spaced inside many random places).

two-up there is no worries about losing the other person... Ectra.

Two bikes = less weight on the bike means less ware and tare. (e.g Tyres last longer...)

HOWEVER the one thing to consider is:
Two up: the toll on the driver. you ride every day for both of you..

you are 100% responsible for the pillion; it meant for me that when normally I would just open the throttle and power/pray that i got though something, (It is amazing how well this works one up).. I could/would not risk the high speed uncontrolled fall, and hurting MrsX. Plus had all that extra weight make this technique harder to try and control.

As I am sure is true for most riders we worry about the other person more then ourselves...

E.G.: One road in Congo/gabon call the FRANCEVILLE ROAD was 250km of deep sandy ruts, deep sand, mud and slop. We estimated that Anubis (our AT) weighted in at more 500KG fully loaded, fulled and two up. It was exhausting for me. Took all the fun out of it.

Finally, is the convoy theory. There are many place in the world that should only be visited by two vehicles (two or 4 wheels it makes no difference). This is in case one breaks down/get bogged ect.... you can get out or send for help.. Two up you are only one vehicle one rider.. we had to chose not to go to some side-trips for this reason. (crossing the Sahara for one example) we got 100k down a piste, it turned in to hardcore desert/dune riding and we had to turn back (after a little bit of fun). We simply could not take the risk of being 200k away from anything and breaking down.

So to sum it up IMHO. If you want to go hard-core off road and to very remote places dont go two-up. Too Risky too hard of work.
If you are going mostly good pistes/sealed roads not too far off beaten track I loved being two up. depends on what you want our of your trip, we would do it again two up.. We like touristy things which tend to be with in our comfort zone of "on the beaten enough track". But if we were to go though the Sahara again we want two bikes.

My biggest piece of advice which either way you go.. is get a decent intercom Spend a good chunk of money on this, two up it was great to chat, talk, directions it was massively important two-up to be able to yell "hold on" or "Big F#$% drop" or what ever and for MrsX to hear me/understand and do it.. save us from many a fall.

One up same reasons but also allows you to keep in touch if not in line of sight.

We used STARCOM1. loved it. StarCom1 Motorcycle intercom helmet audio communication system bluetooth
YES there is days you will turn it off but that is okay...

I know i did not help.. sorry. i think i still debate it.. with myself.

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2000 Africa Twin
http://two-up-ona-twin.blogspot.com