With all due respect to Sheldon and Dan, and to Ewan too, I'm not so sure a wider front tyre than the rear on a bicycle is the wisest thing to do on any bike but especially on a touring bicycle. Oh, it is probably all right for day rides on known roads, if not overdone, but a distant long loaded tour is bound to throw up more stressful conditions and events.
My reasoning starts with two immutable hard facts:
1. On a bicycle, which is inherently unstable -- scope the "bi" in the vehicle name, the roadholding and handling (handling is the capability to save yourself and your bike when it runs out of roadholding) must be provided for the conditions at the limit, which always lurk on strange roads -- by definition the case during distant tours. An example would be a fast downhill at dusk with a suddenly tightening curve with at the apex a pothole you never saw until you hit it.
2. There is nothing as safe as an understeering bicycle, and the more so on a touring bike whose rider will be on a strange road in perhaps unforeseen circumstances when he might be tired and his reflexes less than track-sharp. I've never even heard of a touring or utility bicycle by a designer so incompetent that he made it intrinsically oversteering. This is the reason why experienced tourers go to great lengths to achieve equal loading on the axles. This is also the reason lowrider luggage and fittings even exist -- to arrange the weight transfer couple to slope upwards to the rear of the bike, and for more esoteric reasons of bike stability in crosswinds where a rearward centre of aerodynamic pressure is absolutely essential. Note that a neutral-steering bike is a lethal object because you don't know which way it will break even in casual use when it meets a small extraneous input, never mind at the limit of adhesion. Even bikes with zero use outside the highest level of racing are not neutral-steering: they just have very much smaller margins of understeer,
and none are designed to oversteer.
Your quality purpose-designed touring bike is thus likely to be as safe as can be imagined, the more so if it has a longish wheelbase, when fitted with two equally wide tyres inflated to the maker's recommendation for the load and it's distribution. It doesn't matter whether the designer is a brainiac or a craftsman following and refining time-hallowed practice: the point is that there is an agreed envelope the owner of the bike pierces at his own risk.
Just putting on fatter tyres at both ends than the bike was delivered with will already sharpen up the roadholding and steering through a bigger contact patch with the road, and the handling too, while at the same time distancing even further the likelihood that you will ever require the greater handling. Fatter tyres are faster and safer and more comfortable while at the same time making the bike feel more "sporting", contrary to cycling myth.
Putting a fatter tyre only on the back, all other things being equal, will on smooth roads cause less understeer or, in extreme cases dangerous neutral steer or lethal oversteer as the rear wheel with its greater traction tries to overtake the reluctant front wheel.
Putting a fatter tyre only on the front will tend to cause the front wheel to turn faster than the rear wheel and thus give the bike less understeer. (I know, counterintuitive that the fatter tyre on either end reduces design understeer, but tyres are the least rational part of a bicycle, or a car for that matter.) This, modestly done, could make an unloaded but intrinsically relatively heavy touring bike more responsive to steering inputs. Andy's point in another current thread about the rear wheel being pulled by the front wheel applies. It won't work so well in loaded touring, which is generally weight-biased to the rear of the bike.
The safest tyre choice all round is what the designer intended before the cost accountants started work by fitting narrower tyres than the designer wanted: that is, to fit the fattest tyres the bike will take, same size front and rear and to inflate them to spec for the load and its distribution, and to let the design geometry keep you safe from "going bush" (actually, here in Ireland, into the ditch which lines both sides of the country lanes I love) or landing in front of oncoming traffic.
