As a site administrator, your goal is to attract users to your little spot on the web.
As such, you should seek ways to reach population base that is likely to be interested in your site. There are many different ways to try to do this, but affiliating with other "like sites" is one way.
The question for you is whether the sites complement one another, or whether they serve the same purpose.
If your site and someone elses site serve the same need, then whether you recognize it or not, you are in competition with them for the attention span of the users that you both bring to the table.
You don't want to align your site with another to have "your members" spending more time on the affilate site than your own.
It really doesn't matter what forum software one site runs versus another. What matters is what you are able to offer the users versus someone else.
Here is an example: You run a website centered around perl programming. You offer tutorials, examples, a script library, and a forum, where users get advice from one another.
You could affiliate with another perl web site, which will likely expand the number of potential users who visit your site. However, your users will visit the affiliate site as well. Eventually the users will migrate to the site that best meets their needs. If this is the case, make sure your site is better, and you'll win over their users.
On the other hand, you could affiliate with a PHP website. Each of you would have your core users interested in a particular language, but both would attract people interested in programming. Neither is likely to cannibalize the other.
What software you are running versus someone else is running shouldn't enter into the equation. If so, either you or your members are too emotionally attached to a program.