In addition to the comments from jmort253 I’d also add the following:
If the hours of the internship are not interfering with your new job, and / or the interning company isn't in competition with the new company I would suggest continuing it based on your comments and my thoughts below.
- The new things you are learning in the intern position may end up helping you and your new company in ways you don’t currently know.
- Learning new things is often fun and can keep a less challenging job albeit well-paying job more interesting as you try to find ways to help / improve based on the new things you’re learning, as well as helping you keep from getting burned out if the job is to mundane.
- I've noticed a lot of people that once they get a full time job getting into a technology rut, where their knowledge becomes stagnate because the company is using X technology and will be for several years.
- Keeping the intern position can allow you to stay current and have a broader variety of knowledge to choose from when mission critical issues arise at the new job.
- Lastly you could look at / use the internship as continuing education allowing you to get real world experience outside of your current employer without having to pay the exorbitant fees of your local colleges.
But again I reiterate my first comment, about making sure you have the time for the internship and that it doesn't in any way a competitor to your new employment.