You should notice a bit of an improvement by upgrading to 0.8.0, but even more so if you also upgrade to PHP 7. I've seen significant performance improvements just moving to the newer version of PHP.
There are some improvements around handling row-spanned tables ... but may not enough to make an upgrade worthwhile. In the next version or so I'm hoping to see us make improvements in that area.
As for the actual upgrade process? I would probably start from scratch. The format of the font family cache file has changed and so you're less likely to run into font issues if you start clean. Note that the main project no longer supplies the load_font.php file, though you can find a version in the utils project
that should work with 0.8.0. The method of configuration has changed significantly since (as of 0.7.0) dompdf no longer uses the dompdf_config.inc.php file. And also there are changes to the dompdf-instantiated FontMetrics class used in inline script.
If you have any more specific questions or concerns please let us know.