We always recommend the Offline installer. Yes the offline installer will keep the version it is. The online installer installs the present version. Since the older version is no longer on their download server, you will be directed to present version. To save it ... I normally keep them on an external drive or DVD-RW.
Often installation errors can occur when installing online. Packet loss, etc. ... any interuption in the installation process. This is a common problem with Java. Corrupt java installations due to being installed online.
Oh another point about the online installer is not all data comes from the LW site. Some of it comes via the gnutella network. This reduces stress on the LW site servers. You may find in your preferences folder a partial update file ... that's shared for when other people are updating their LW's. So you are helping them install. This process in itself may be an issue with problems with installation. So at least with Offline installations ... all the data is already within the installer .. none of it being sent over the internet ... the installer not needing to wait for data from wherever else it may come from.