The most important thing is for the OP to try out some cameras beforehand and get something they find easy to use. It is no point getting the best reviewed camera for your budget if you find terrible to use.
I agree that dSLRs are better for low light shooting and fast moving objects but I disagree about the telephoto ends of the superzoom cameras being of limited use. In decent light they are more than capable of focussing fast enough. The LX3 has a pitiful tele end range and if it even had an 85~100mm equivalent it would be much more useful IMHO.
Regarding the Eagle picture even a low end dSLR like a A200 or D40 will not have fast enough AF unless you have an SSM or AFS lens . With budget or older lenses in low light there can still be issues with hunting too especially with faster moving objects.
I have used plenty of these "so-called" inferior compacts and have got many fantastic pictures out of them.Many of them did not have any stabilisation either.
To overcome the lack of stabilisation in low light I either used a monopod or rested the camera on a solid surface if I could not be bothered to carry the former.
However their small size meant that I had the cameras to hand in situations where I would not be carrying a film SLR or a dSLR.
I also disagree with this almost snobbish derision of compact cameras. Better cameras make the job easier(and sometimes open up new opportunities) but still even such "lowly" cameras like the Canon A620 and A80 are capable of producing great pictures if used properly:
http://photo.net/photodb/presentatio...tion_id=317651
http://photo.net/photodb/presentatio...tion_id=273356
Also you bring more attention to yourself waiving around an SLR which is not a great idea in many cases. People either think your are loaded or some professional especially outside of more affluent areas in my personal experience. You are less likely to be bothered when carrying a compact especially if you want to take some candid pictures.
The less the OP can carry the better. Either you they will be stung with high humidity at sea level or very thin air in the mountains which can really wear you down especially if you are trekking.
I have known people who have gone to Machu Picchu and even travelling light it can be a very tiring journey if you are trekking there.
Of course if the OP is some super fit athlete then perhaps this would not count as much.
Is the OP looking at this as a photography trip or trip with some pictures taken on the way?? If it is the former I can agree why people would be bothered to lug around a dSLR. If it is the latter and you are travelling with some mates there would situations where a dSLR would be overkill(for example on a night out in one of the cities for example).
If you are travelling it makes more sense for the average photographer to have one superzoom covering a larger range too. However a superzoom and an A200 or D40 will far exceed the budget of the OP and also the 28mm end of these zooms is not enough IMHO. Something closer to 24mm(in 35mm terms) at least is preferable. Zooms like the Sony 16-105mm and Nikon 16-85mm are well over £300!
Especially with the amount of dust and humidity in many of the countries the OP is travelling they really need to be carefully about changing lenses too if they are a novice and also must know how to clean the sensor if they do get anything on it.