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Yes it is entirely possible. I have done it with my site (see my signature). As for step by step that is a bit harder because I have been playing with XOOPS for 2 weeks now so it all blends together.
However, something like this;
1. Install Xoops.
2. Get the X-PHPBB module files.
3. The install of X-PHPBB takes about 30 minutes and requires the copying of all of the files up to the server.
4. There is a converter script that will grab your users, topics, posts, forums, etc from your old installation and import them into the module. IT works very well.
5. Troubleshoot any problems. You will find some things you don't like and need to fix them. I found that the porting across busted my Polls because there was a data issue. Just about any problem can be fixed.
6. Go to the BBPixel forum for support.
As for which is better that will be long debated.
The advantages with Newbb are that;
you only have one search system not two.
it does integrate better but X-PHPBBM is quite good as well.
Your pages are produced with better more standards compliant code.
With X-PHPBB,
I personally think it looks better.
it probably has more features
Your page code is faulty. You end up with two HEAD sections and BODY sections on your Forum pages. Would love to solve this one.
Bottom line, both are good and both work. There are however better converters if you stick with PHPBBS/X-PHPBB. That situation will likely change over coming months. Question probably is how long can you wait.