According to Apple Mountain Lion has more than 200 new features that they will cover if you go to their web site. Otherwise, the difference is one "Mountain" and a different cat.
Lion is no longer supported. You cannot upgrade to Lion unless you have a computer model that cannot run Mountain Lion. Mountain Lion provides stability, security and performance improvements over Lion.
Any time you do a system upgrade there is a risk that data will be lost or corrupted. There's the risk that the data is already corrupted but you were not aware. Then you upgrade and the computer no longer works at all. And, you didn't make a backup before you started. Up the proverbial creek without the proverbial paddle. So, if you are thinking about stepping off the cliff:
Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu. Restart your computer.
Open App Store in the Dock and sign in with your Apple ID and password. Locate Mountain Lion, purchase, and download it. The rest is automatic. Once Mountain Lion is installed the installer will delete itself. So, BEFORE you click on the Install button make a copy of the installer (in your Applications folder) and put it in your Downloads folder just in case. Later you can think about making a bootable flash drive installer:
Make Your Own Mountain/Lion Installer
1. After downloading Mountain/Lion you must first save the Install Mac OS X Mountain/
Lion application. After Mountain/Lion downloads DO NOT click on the Install button.
Go to your Applications folder and make a copy of the Mountain/Lion installer. Move
the copy into your Downloads folder. Now you can click on the Install button. You
must do this because the installer deletes itself automatically when it finishes
installing.
2. Get a USB flash drive that is at least 8 GBs. Prep this flash drive as follows:
a. Open Disk Utility in your Utilities folder.
b. After DU loads select your flash drive (this is the entry with the mfgr.'s ID and size) from the left
side list. Click on the Partition tab in the DU main window.
c. Under the Volume Scheme heading set the number of partitions from the drop down menu to one.
Set the format type to Mac OS Extended (Journaled.) Click on the Options button, set the
partition scheme to GUID then click on the OK button. Click on the Partition button and wait until
the process has completed.
d. Select the volume you just created (this is the sub-entry under the drive entry) from the left side
list. Click on the Erase tab in the DU main window.
e. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, check the
button for Zero Data and click on OK to return to the Erase window.
f. Click on the Erase button. The format process can take up to an hour depending upon the flash
drive size.
3. Locate the saved Mountain/Lion installer in your Downloads folder. CTRL- or RIGHT-click on the installer and select Show Package Contents from the contextual menu. Double-click on the Contents folder to open it. Double-click on the SharedSupport folder. In this folder you will see a disc image named InstallESD.dmg.
4. Plug in your freshly prepared USB flash drive. You are going to clone the content of the InstallESD.dmg disc image to the flash drive as follows:
a. Double-click on the InstallESD.dmg file to mount it on your Desktop.
b. Open Disk Utility.
c. Select the USB flash drive from the left side list.
d. Click on the Restore tab in the DU main window.
e. Select the USB flash drive volume from the left side list and drag it to the Destination entry field.
f. Drag the mounted disc icon from the Desktop into the Source entry field.
g. Double-check you got it right, then click on the Restore button.
When the clone is completed you have a fully bootable installer that you can use without having to re-download Mountain/Lion.
Note: The term Mountain/Lion used above means Lion or Mountain Lion.
As an alternative to the above (you still have to do your own download of Lion/Mountain Lion) you can try using Lion DiskMaker 2.0 that automates the process of Steps 2 through 4.