To me clicker training and marker training are one in the same. There are some classes here who advertise clicker training, but actually tend to use a marker word more in class settings just because there are so many dogs at once trying to learn.
As to which class the OP should take, for me it would depend on what methods the other class was using alternatively. Is it a non-food class taught with dominance and fear based methods? Is it a fun class that rewards the dog but just without the use of a clicker? Is it a class that starts puppies out on choke chains and is ready to correct before actually teaching? There are many different methods out there.
As far as what training method is best: That depends on the owner and the dog. There are lots of different methods out there. Personally, I love marker training. Shaping is a lot of fun inparticular, and for that, I find the clicker works best. The dog thinks and decides for itself what behaviour gets the reward, and thus, IME, learns faster. Shaping also provides the chance to teach tricks that would otherwise be much more difficult if you were trying to lure, but shaping isn't for everyone (takes some patience and a passion for training). Either way, whether I'm shaping or luring, I marker train. I find that if I'm teaching something where I don't have to focus too much or hold a leash or anything, the clicker is my 'go to' tool. In other circumstances where I do have to focus more/hold a leash/don't have a clicker with me and want to teach something, a "yes!" works as well. I find that when I use "yes!" instead, the dog is more excited, but their learning rate slows just a tad. No matter how I try to time my "yes!", for me, the clicker is always more accurate and consistent. That said, both work just fine for me. And even while I'm using a clicker, I still praise my dog with a "yes! Great job!" or "excellent!!" or something. Not really on purpose, but I just can't train a dog and keep my mouth shut haha.
As someone who prefers positive training methods: I am not completely against the use of correction. Some positive trainers are, but I've lived with a lot of dogs, and honestly I can't imagine trying to train a couple of them at least without a correction at some point in their lives. So sometimes I believe dogs do need correction, and this is dog dependent on what the correction would be. But I will not correct until my dog knows a behaviour 100% and I can see that they're just being jerky about it. I also prefer to set my dog up for success whenever I can. And like I said, I wouldn't go to a class who was all or mostly about corrective methods before building a good positive foundation. A good friend of ours once said something several years back when we first met her along the line of "The dog was so good, I had to set him up for failure just in case he ever decided to counter surf himself. Better to have him know now that it's wrong than to wait for it to happen". That is something that's stuck in my head since I met her, and while I love her, her training methods and mine do not mesh. I just don't understand the mindset of setting a dog up for failure rather than setting a dog up to be successful.
Basically, I approach dog training how I myself want to go through life. I don't want to constantly be nagged and told I'm doing something wrong and to do it better without anyone actually showing me what to do. I don't want to play guessing games, and I don't want my dog to feel like she's playing a guessing game either. Instead, I want to be told when I'm doing a good job, be let known when I'm doing something wrong, but shown how to do it better in an educational way. And that is how I choose my dog classes. Whether they use marker/clicker training or not, I want a class that is going to support dogs and set them up for success and give them a paycheque when they're doing something right. You can train positively and successfully with or without a marker. I just would not go to a class who did not use food or was quick to correct.
I grew up learning how to train dogs in what I consider to be a relatively positive manner. They were lured into behaviours initially, rewarded with treats/praise/play when they did it right, were told throughout their lives when they were doing a good job, etc. No clickers or marker words were used (or not purposefully that I can remember), but it was still an effective method. The dogs knew behaviours, listened when told, etc. This is the method I find many dog classes around here tend to use still. I do think my dogs growing up were told they were doing wrong too much, and that's still something I watch myself with (old habits are hard to break), but still, whether you use a clicker or not, you can train positively and effectively. I just find a clicker gets faster results, so that's what I opt for. Especially for puppies who are little sponges!
Anyway, hopefully some of that makes sense! I tend to ramble sometimes haha. It makes sense in my head, but sometimes it's hard to convey in type.
Also, to whomever said that clicker/marker training causes behavioural problems, simply put: no, it does not. Marking a behaviour when teaching a specific trick/command/whatever you want to call it is ALL a clicker or a "yes!" does. Marker training does not create ill behaved dogs with no manners. That depends on what a person tolerates IMO. Just because I train in a positive manner and prefer to immediately mark a behaviour for better success and a faster learning rate, does not mean that my dogs are running wild and rampant and behaving poorly in every day life. My dogs are very well mannered, wonderful in the house, and well trained. They listen to me with or without a cookie, because I have expectations. The fact that they are marker trained has not negatively influenced them at all. It's a HUGE pet peeve of mine when I see people try to blame positive training and clicker training for some peoples' dogs' behaviour problems. I agree with those that have said positive does not equal permissive.