Yes, it's worth the effort. As long as you have the time to mosey on over.
Generally the ticket needs to be endorsed by the issuing carrier over to the other carrier you want to use. This is usually no hassle if you are on a full fare (like Y or F class) or even one way reduced coach fares that don't require advance notice (like 3 or 7 days) for changes.
Getting into advanced booking/ticketing fares gets a bit more restricted and may not be allowed changes - unless of course you are willing to pay the applicable penalty for doing so.
The key here is to have the ticket "endorsed" over, because just walking over to another airline does not necessarily keep it a negotiable instrument. Here's where travelers might see the wisdom in paper tix instead of the e-tickets. I'm certainly not against e-tickets but the paper is handy in a tight spot where time is a real constraint if you have to quickly get it done from one airline to another.
Good luck, Misstree.