The immediate impact with a collaboration is simply attempting to share each others audience. But that is a very simplistic approach to a tool that can be far more valuable than the immediate gain of a handful of subscribers.
I have done some collaborative work, and even work with a group of like-minded fishing channels. As a collaboration we occasionally fish together and that's fun because it presents our content to an audience who likes what we do but may not be familiar with us. It is also valuable to see someone elses presentation of the exact same content as a means of learning what works (and what doesn't). But it is the behind the scenes stuff that is in my opinion most valuable. With a collaborative group you can help push each others videos when you have something that you are really proud of; it obviously can't be done every video but when you have that one that you really want to shine it's nice to have a group who will help push you on various forums, via social media, community tab etc. It also helps when someone else endorses your work.
Beyond the videos though my group is also great about bouncing ideas off each other and we help each other with insight into our editing, thumbnails etc. We all started Affiliate marketing together, and we all suffered the lack of sales in the first few months that caused us to have our accounts closed... now we all purchase from each others links and because we do Sports/Outdoors we are often hit up by Amazon sellers to help promote their products, which we purchase off each others links as well.
So in synopsis (because I am WAY too long-winded, sorry) a collaboration done correctly can wield a lot of benefits for your channel.