Like @andybond says, styles and add-ons from 1.5 do not work in 2.2, so you will need to find equivalents. I'm happy to say that of the add-ons we use on ours, I was able to replace all the add-ons with new ones that were even better than the originals. Some I had to pay for, but they are also from developers who have been around for a while and regularly update their add-ons.
You will see the stock XenForo 2.2 style after you upgrade. Any template edits you have now will be lost, as they are incompatible.
Your style settings will also be lost.
But, your board options will all remain in place. As will your warnings, trophies, user ladders, user upgrades, usergroups, etc.
Set up a dev board in 2.2 and style it. You can manually bring the style settings over and style it pretty close. Then look for 2.2 add-ons that you will need.
Set up a dev board in 2.2 and style it. You can manually bring the style settings over and style it pretty close. Then look for 2.2 add-ons that you will need.
^ This. Our license allows for one additional forum installation secured behind an additional login (an htaccess password, for Apache users--other web servers have a similar feature).
I've had a test forum running for 15 years and use that to develop add-ons and styles. (We converted to XenForo originally in 2012.) I no longer do template edits--all my changes are done through template modifications which I build as installable add-ons. That way, I can export the child styles I have created with all of my changes, then import them into the live forum, followed by installing my custom add-ons. It cuts down on time and grief by having everything be installable.
From there it's just a matter of going through all permissions and settings, as there are new features and permissions that XF 2.2 has over 1.5. I'm about to do this same upgrade on two forums within the next month. Fun times ahead!