I made a more complete list of two types of fork scenario:

Hard fork is a loosening of the rules
If minority of hash power upgraded to new version, then new blocks will be orphaned
If majority of hash power upgraded to new version, then there will be two incompatible chains (like march 2013 fork)

Soft fork is a tightening of the rules
If minority of hash power upgraded to new version, then there will be two incompatible chains (like July 04 fork)
If majoriy of hash power upgraded to new version, then old blocks will be orphaned

So both upgrade will possibly fork into two incompatible chains depends on situation. But if you always make the upgrade when majority of hash power is supporting the upgrade, then soft fork can make sure there will not be two incompatible chains, while hard fork will create two incompatible chains at first

However, when you have the major hash power supporting an upgrade, then the miners of the minority chain in a hard fork can not mine without suffering huge loss on the mining income (too slow mining), similar to the minority miners in a soft fork suffering huge loss when all the mined blocks are orphaned. So hash power will give up the minority chain quickly thus basically achieve the same result: After a few days, no one would be able to extend that old chain in any meaningful time. This has happened on that "50 bitcoin forever" fork during the first reward halving