Usually, this works without too many problems, but it's by far the most dangerous way, meaning you could hose your system. Because if the upgrade goes poorly, you're going to have to upgrade with a clean installation of the latest version of Ubuntu.
Linux Mint, by contrast, doesn't offer the fancy option of a distribution upgrade. Instead, they suggest you use mintBackup, then do a clean installation of the new release. As one might expect, most people tend to lean toward the Ubuntu method since it takes less work. Some might even argue that it's easier, too.
I would suggest that distribution upgrades that don't provide a default installed GUI software backup tool are really rotten.
Personally, I think it's a crime that both distributions don't default to dedicated home directories. It's so simple, I honestly fail to grasp why this isn't offered to newer users.
Having a dedicated home directory is fantastic. Should I hose my system somehow, I simply reinstall the Linux distribution and all of my personal data remains on the system.
The best distribution is...
By no means, am I going to claim that either of these distributions is the best option for all users. First of all, some users are happy with Arch Linux, Slackware, or another Linux distribution entirely. For those of you looking to better understand what really makes Linux Mint different from Ubuntu, however, this article hopefully is be food for thought.
Contrary to what casual technology pundits out there will claim, there are stark differences between Linux Mint and Ubuntu. So before anyone makes the claim that they're basically the same, I'd suggest re-reading everything I just shared above.
For Linux users seeking stability and safety with their desktop, Linux Mint wins the day. If however, you're someone who waits anxiously for the next release of their favorite operating system to be released, then Ubuntu is going to be a better match for you since it's released ahead of Linux Mint.
Speaking for myself, I prefer to dual-boot both distributions. Since I'm able to dual-boot using the same home directory, there's no need to choose one Linux distribution over another.