I rode the older F650 Europe to Asia, and am currently in the middle of DC-Alaska-Patagonia on the new F650GS (non Dakar version - although I did test ride the Dakar). This is a bit long - sorry....
The range on the old bike with the 27 litre Acerbis tank was (as egreen said) fantastic - 500+ km/300+ miles. The new F650GS range is around 320 km/200 miles fully loaded and going fast (130 km/80 mph+). Reserve kicks in around 160 -180 miles. On the other hand I got around 400 km/250 miles range going slow speeds on easy dirt. But tougher off-road trails got closer to the 200 miles range.
Fuel injection on the new GS is fantastic on the road - very smooth and fuel efficient. The teething problems with surging and stalling have gone away on my May 2001 (frame date) bike. New software is continuously released and gets updated whenever you service the bike.
I used all sorts of gasoline in the older F650 - never a problem - but it did lose power in the higher mountains. I had an inline disposable filter - something which is harder to put on the new GS/Dakar (presurized fuel system). The new GS is great in the mointains - automatically adapting to the changes in air pressure so no real power loss and actually a fuel economy gain. Have not yet tried the really dodgy petrol out of 40 gallon drums but it runs great on all octanes so far.
The cat-converter exhaust can be 1: replaced by a regular exhaust (Staintune), 2: the cat insert can be removed (but you will need a TIG welder) from the exhaust or 3: a senior BMW guy told me that you can just leave it in there and it will just run hotter on leaded gasoline. (have not tried that yet)
The new stock GS is better than the old 650 for me off road, and the Dakar with the 21 inch front tire is better still. A fully loaded water cooled BMW is never going to be the lightest thing off-road, but they are manageable nonetheless. (It's my belief that off-roading is much more about the rider than the bike - witness the guys with loads of experience doing the haul road to the top of Alaska in harleys and goldwings.) These 650 bikes will help you a lot when you go off road, but its still all about experience (which I am still getting...). I went part way on this trip with a novice off-roader (on another 650GS) and she was able to pick it up very quickly (albeit with a couple of minor spills).
Speaking of spills, the lower center of gravity on the new GS makes picking up a fully laden bike no problem.
On road in the twisties these bikes can keep up with most road bikes. And they are unbeatable around town. The dakar has noticeably less braking power on road (that 21 inch front) than the standard GS and the older 650 - if you are a faster on-road rider and/or heavily laden then this could be an issue.
The ABS system has improved tremendously over the years - it seems very mechanically simple now and is integrated into the wheels whether you like it or not - indeed the speedo seems to run off the rear ABS system. I've had no problems with ANBS so far on the new GS. (and it has also come in handy a lot on the road) You can turn it off for the really loose stuff. The 2002 Dakar now has ABS as an option - well worth the extra $500.
Both of these bikes hold together well - they don't require the same amount of constant tightening of nuts and bolts as the XT or KLR say. They are also very smooth to ride all day.
I get mine serviced at BMW dealers (they are everywhere but expensive - aim for the countries where labour is cheap) and really don't carry any spares - you can always get them sent or machined locally.
Make sure you put fork boots on the front (they are cheaper than replacing broken fork seals)
The heated grips are a "necessary luxury" but unreliable as anything - all mine have failed.
I've dropped both bikes (off road only) and they bounce back ok - no expensive damage. (The happy trails aluminium case system works particularly well - they pivot in a drop)
F650.com is a huge source of information.
My older F650 also had battery issues. You may be able to get a Hawker battery (Touratech were trying to source it for the states). No problem with the GS battery yet - and 24000+ miles/38000 km on the clock on this trip so far. It is buried under the fake tank so I don't check it as often as I should.
I've been riding solo but also had 3 weeks two up - The bike was great 2-up as long as the speed and weight were low - which is the point... Enjoyable ride on and off road.
see you on the road....