Hi Jens, I think everything has been covered, but just wanted to weigh in with my 2c. First up, as a predominantly film shooter myself, I just wanted to say you're making the right decision to go digital for the trip. The freedom to take as many photos as you want without worrying about processing costs, xray machines, availability of film, ease of sharing photos etc can't be underestimated. Plus, you'll probably be surprised how good digital is compared with film these days. Its no longer a competition. However, as mentioned above, there are new challenges, including batteries, backup storage, security, should you take a laptop with you, raw vs jpeg...I'm sure you'll have fun figuring out your own solution.
On to serious matters. You've inadvertantly stumbled onto the deep, dark secret of the camera industry. In well lit conditions, a camera phone can take a photo that is as captivating as a full frame camera. Canon and Nikon jointly fund a PR company to deal with problem people like yourself. I'd be expecting a knock on the door any moment from someone offering hush money.... So why go full frame with the 5Diii? Marginally more background blur. Better image quality at high ISO's (and if you look really closely, better at low ISO's too). A little bit less "noise" in dark parts of your photo. Comparing your two cameras, the 5D will have better autofocusing and subject tracking abilities (not that the 650D is "bad') and will be less likely to break if you get some rain on it (although, I'd be very surprised if the 650D couldn't withstand a few drops). The 5Diii is a better camera and at the extremes, you will be able to take photos with it that the 650D will struggle with. Do these differences matter to you and are they worth the price increase? Some people say yes. Many say no.
One of the earlier posters raised a very good point. If keeping the 5Diii impacts on your ability to fund lenses (or have an enjoyable trip), I know which way I'd lean. Also, I get the impression that you're a little older than the average Canon Rumors poster. If that's the case, I'd be really wary about weighing yourself down with a lot of camera gear unless that's the driving focus of the trip. Anyway, have fun!