I don’t live in the UK, so I’m not familiar enough with the candidates to pick a likely winner. I can, however, make a prediction as to how the battle will be won.
The Conservative Party, as it exists today, is a coalition of two groups with fundamentally incompatible ideas about what the government should be doing. One of these groups wants a small, agile central government that cuts taxes and regulations, signs trade agreements, and focuses on economic growth. The other believes in a robust welfare state (particularly for the elderly), protectionism, traditional values, and limits on immigration. It wants a return to the glorious past, not a trip to the future.
The way to reconcile these two groups is to separate style from substance. Donald Trump was an expert at this. The new leader will speak loudly and constantly about culture war issues–in particular, hitting themes about British patriotism and the forgotten people in small towns outside of London–while actually governing as a tax cutting liberal. That’s the only way to keep the band together.