If I understand you, you want to know the differences between persistent USB and a full install USB.
Persistent Live USB: 8GB or more
First, Persistent Live USB takes less space.
One can create a non-persistent Live USB with a 4GB USB drive. To create a persistent Live USB you would need a slightly bigger one, say 8GB.
Second, Persistent Live USB can be used for installation.
A persistent Live USB is essentially a copy of the installation DVD. The files in the original ISO remains as is. Updates and future installations are saved in the space designated for keeping the changes. Say, you update Firefox. in a normal installation the old one is replaced. In persistent installation the old one stays as is, the newer version is located in the persistent virtual disk (within the USB) taking up extra space and sometimes creating problems, for example for kernel updates. Now if you install Ubuntu from this persistent copy into another hard drive the original version of Firefox in the DVD image will get installed.
Booting a persistent Live USB gives the students access to the "Install Ubuntu" icon on the desktop. Students can "accidentally" start the install process and delete the contents of the hard drive.
Third, Persistent Live USB is less secure.
There is no login process in the Persistent Live USB. The default user has admin rights and does not need a sudo password to exercise it. This means, a malicious student can boot a persistent USB of another student and easily access stored documents, uninstall or reconfigure applications etc.
Fully installed Ubuntu in an USB: 16GB or more
First, Installation takes more space than keeping the image of the installation DVD, about 9GB.
Once installed, the system can be updated, and customized. Uninstalling unneeded software will free up space.
Second, Hardware on which the full install is created is important.
The Live DVD image in the persistent USB is created with compatibility with most computers in mind. However, once installed on a specific hardware, the installation gets a bit customized for the specific components. This is important particularly if the computer has some parts that require proprietary drivers. Once these drivers are installed, the USB may not work on computers that do not have those specific hardware. Conversely, if the installation is done on a computer that does not need any proprietary drivers, that specific installation may not work on the machines that do need them.
Therefore, if the goal is to use the USB in different computers, a persistent Live USB may be a better choice than a full installation.
Third, Full installation is more secure.
Creation of an user ID and a password is required during installation. This password is needed for any administrative action. One can also set it up to require the password at login.
Also see Difference between LiveCD, LiveUSB, full-install, and persistence?
Hope this helps