So lets start with aesthetics. Solid core doors look fabulous, and just like the feel of a fine fabric in your hand you will also feel the weight of the this door. Nope you won't be holding the door fully in your hand but don't think for a second you won't feel the weight and importance of that door. Also because it is a solid piece of wood you can stain the door as well as paint it. A solid door will provide a great deal more privacy by lessening the sound that one can hear through the door and it is also a great deal more fire resistant so you can feel a lot safer concerning a fire moving into your bedroom space while you are sleeping. Solid core doors are very heavy and do not come in a frame, and therefore your carpenter will need to install the frame itself and then the door has to be installed into the frame which is obviously more labor intensive. You can get the solid wood doors already carved in the design you want or you can place your own wood moulding on top of the door.
This is a kitchen in a house where we installed solid birch wood doors, installed the moulding on top of the door, and then stained the door.
Here is the master bathroom showing the ladies vanity area and the solid core door to the left. It has a gloss finish on the door. As you can see we applied the moulding onto the door.
Hollow core doors are affordable and easier to install because they come with the door frame already attached. Although of course you can buy an individual door without a frame, if you only need to replace the door itself. Hollow core doors are just what they sound like, they are hollow, so obviously much less expensive than a solid piece of wood, they also aren't wood, but rather a composite material. Hollow core doors are a great economical choice and they come in a variety of panel configurations in which to choose from.
Below is an example of a hollow core door. It looks great, it does the job and it is about half the cost of solid core doors. You can see a tour of this house by going here.