There would be 'two' difficulty levels, one exactly half of the other. The highest difficulty level would adjust until the block generation rate was every 10 minutes regardless of the mining reward.
If you accepted half of award, you would be able to submit a block at the 50% difficulty level. If everyone moved to half the block reward then you would still get 1 block every 10 minutes at what ever difficultly level exists based upon competition of miners for 12.5 vs 25.
There is no point in doing that, everything would be exactly the same - miners would make as much money and the same amount of hashing would be done.