Short answer: It depends
The alcohol only burners are built differently than the Kerosene burners which can be made to run on either Kerosene or alcohol.
Burner on the left is a Patria 206 Kerosene burner the one on the right is a primus alcohol only burner. You will notice that the kerosene burner has additional piping that provides more heated time to the fuel
before it gets to the jet which allows the kerosene to vaporize properly. That said, it is not uncommon for an alcohol stove
to have the Kerosene type burners on it and just be fitted with the jets for alcohol. If that's the case, a simple jet swap and you are off to the races.
If not than you need new burners which is not that big of a deal either.
I did a post on my conversion over on sailnet that you can read here: Conversion of a Kenyon 206 Alcohol stove to Kerosene - SailNet Community