Okay let's make this really simple, taking the article (regardless of how exaggerated it may be) as relatively accurate. There are several consequences from the two actions that could happen. I've even made a little chart for you.
If the man is guilty, as in he willingly committed said actions, he is given a "fair punishment" by the laws of China, it's a blow albeit a rather small one against smugglers and obviously he won't do it again.
If the man is "innocent" meaning he was not capable of making rational choices due to a mental illness as opposed to excess of alcoholic substances, fatigue or drugs, we are left with a man, who suffered with mental difficulties, dead with a great injustice being served. Political tensions between western nations, especially the UK would worsen and potentially civil unrest in the form of protests and so forth. You saw the stir raised because Gary McKinnon was extradited - thing of a country killing a foreign national.
On the other hand and he is sent back to the UK for a fair trial, he may be placed in prison if found guilty but if proven "innocent" he will be given the help he needs.
Now the risk of him being innocent and being killed by far is much more damaging than the risk of him being guilty and being executed. It's far safer to take the "back to the UK" path.