I was an instructor last year and here is what I have from my experience.
If you go on a busy day (weekend, holiday), splurge on a private lesson because there can be tons of people taking beginner lessons. When you take a private, you SHOULD have the opportunity to request a specific instructor. If you can ask around (tickets, rentals, even the person who is helping you buy a lesson) they may give you a name or two... usually if you request a specific instructor, they will make more money (it will not cost you more) than if you are randomly paired for a lesson. DO THE INSTRUCTORS A FAVOR AND REQUEST ONE BY NAME. These people usually are required to be at the mountain from 8 to 3, but often only get paid for hours actually teaching. I spent many days with no lessons, only getting paid for a single hour. Just by you requesting them by name can be the difference between 9 dollars an hour and 25 dollars an hour (with no change in cost for you, the student.)
Another advantage to private lessons: building a relationship. Stick with someone you like and they will help you progress faster than a random instructor in a group lesson. Also, make sure to tip them after. Many people don't tip, because they are already bummed about how much the private lesson costs. But if you throw your instructor a 10 or 20, and ask him/her to take some extra runs with you after the lesson, they should hook you up. If I had nothing else to do, and my lesson just tipped me $20, you know damn well I'll be spending another hour with them honing their skills. If you get the vibe that the instructor is a newbie, this may not work but any veteran should get the idea. Snowboard instructors are pretty much like strippers... we'll do almost anything for some extra cash... take you slow, fast.. give you some extra time... spin... flip... show you the backside...
You can always take a look at the group lessons, but just make sure you get a look at how many people will be in the lesson by finding the meeting area and seeing how many people are waiting. If you are not riding during peak times, you can get away with taking a group lesson and most likely, there will be 2 or 3 other people in the class, which isn't a big deal.
I think that the most important time in your progress as a rider to take a private lessons is when you have reached a plateau (usually going from beginner to intermediate and intermediate to advanced). Once you learn how to turn, you have to get comfortable with where you are to get better. If you are not comfortable enough to push yourself to try new things, then a lesson will not benefit you a whole bunch. I would often have lessons that were at a certain point, but were not comfortable going faster, or making tighter turns, or tipping up on that edge to carve better. This makes it very difficult to progress. In other words, make sure you are READY to move on before you spend money on a private lesson. If you are TRYING to go faster but can't, or if you are TRYING to ride steeper trails but are having trouble THAT is the perfect time to take a lesson.
Final verdict: Take what you learned and apply it on the hill. Get comfortable to the point where you want to push yourself to do new things on a snowboard. Try some new things on the snowboard, steeper trails, tighter turns, etc. Identify where you are having issues (make a list of 3 or 4 things you really want to get better at). Request a private lesson from an instructor that you have heard about. I promise you will get much more out of that process than if you just sign up randomly. But hey, this is just if you are trying to save some moolah. If you have the cash, nothing is stopping you from getting a 6 hour private lesson.