Do Not Pass Go, Skip Straight to SharePoint 2013
It's based on what Microsoft defines as a migration. A SharePoint migration involves copying and moving items from a database but not the database itself. All the unstructured data, structured data, other attributes and important SharePoint "stuff" can be read or copied. Everything is then reproduced in a different database on a new SharePoint farm.
If you use a capable third-party SharePoint migration product, you can achieve this with no dependencies or limitations related to the SharePoint version being migrated either from or to. A SharePoint migration also allows items to be moved in a more granular fashion. They don't have to be moved to the exact equivalent location in the new SharePoint target. You are free to exercise your creative nature and your observations of the usage of your existing SharePoint, and move to a new structure that actually fits how your users wish to use SharePoint to more effectively meet the business problems that you are trying to solve.
Using a migration tool also means that you can instantly take advantage of new features and capabilities within SharePoint 2013. Instead of starting with a blank canvas in 2013, you can apply its new features to your existing content. This is especially useful if you previously had to use a costly customization in your old SharePoint to solve a functional gap that has now been filled in the new SharePoint release.
By using migration, there is no version gap too wide for your move to SharePoint 2013. You can skip directly to SharePoint without any completely unnecessary and costly intermediate steps.
Take the express route to your SharePoint 2013 destination.