Having a drastic difference in grip between the front and rear axle is highly unadvisable. Avoid this situation if you can at all help it.
When it comes to fitting two new tyres (whether it be summer, all-season, winter or snow tyres) to whichever axle, let it be clear there is no such thing as "the better" option, it is more about the "least worst" option.
The German Automobile Club (ADAC) conducted a test, by fitting gripper tyres on the FRONT axle, and ended up with the following results:
Pros
- Reduced aquaplaning when cornering.
- Significant reduction in braking distances when slippery.
- Slight reduction in braking distances when dry.
Cons
- Significant likelihood of snap oversteer (on cars without ESP).
- Likelihood of snap oversteer on cars with ESP is reduced, but if the limits of the ESP are breached (they cannot bend the laws of physics) then the ensuing break in traction tends to be more violent and uncontrollable.
The conclusion reached by ADAC is to fit gripper tyres on the rear axle. Hence, the recommendation of tyre manufacturers and motoring organisations stems from their goal to prevent any situation which could lead to snap oversteer in slippery conditions, which in their opinion overrides the benefits from fitting gripper tyres on the front axle. Essentially, their priority is ensuring and maintaining stability on the road.
My opinion - you're pretty much f***ed either way.
However, different drivers have different priorities, and if you're intelligent and mature enough to look all the facts, and take into account local conditions, then you can probably make your own decision accordingly.