When v4.3.2 is still installed (as Windows service) the v4.3.3 installer fails to install a new service.

The reason is as follows:
In all previous versions the service's DisplayName was Atlassian JIRA 4.x.x and a new installer would simply add another service with a new version number.
For some reason this has been changed in v4.3.2, the Display Name is now Apache Tomcat 6. As a result, when a new installer tries to install a new service, this fails because a service with that DisplayName already exists.

Workaround 1

Update the service name as per the attached screenshot. The service name comes from the existing service.

Workaround 2

Rename the v4.3.2 service in the registry:

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\JIRA260411164010\DisplayName = Atlassian JIRA 4.3.2

(On my machine this setting did not take immediate effect, I had to open and close the service's properties in the control panel first)
After that, the v4.3.3 installer can successfully install the new service.