Volumes have been written on these two tools in Photoshop and hundreds of websites abound with information on how to use them.
Allow me to over simplify. Levels is a good intermediate tool to quickly make adjustments to an image. Curves will allow a great deal more control in achieving precise results and will require a bigger learning curve.
Way over simplification I know. Practice with tutorials and reading the articles, in print, web, or owner's manual, about how to use them. Amazing results are possible.
And, I would use these tools as an adjustment layer rather than straight off the Image>Adjust menu. That way you can make changes at will at any point in the process.
Which one do I use the most? Depends, yah I'm ducking the question. I will try levels first and if not happy with the easy solution there go to levels where I have more control. If I need to hit a color on the nose I use curves.
I also use the history brush a lot. I'm lazy. Precise control throughout an image can be achieved using curves. I'm not even close to being that good. So, I might adjust for something specific, over doing everything else, take a snapshot, go backward, and then use the history brush to paint back what I want adjusted.
Some argue that LAB color space offers more control than working in RGB. In LAB you can control, using levels and curves, the red/green and blue/yellow channels separate of luminousity channel.
Short of researching and practicing there is always Robert Sanders Photo Intensive Workshop.