Pine is lighter, cheaper, dings and breaks much easier than oak. Oak is a hardwood and is quite durable, and looks very good when stained well. Staining it isn't usually difficult (pine is more difficult to stain well). Just take your time, wipe off any excess stain, and just apply it again after it has dried if you want it darker. Then you can oil it or coat it in clear (brush-on satic polyacrylic works great in my experience).
We installed hardwood floors and have a lot of wooden furniture in our house, and oak is our preference. There are other nice hardwoods, but we like the heavy grain of oak. Quality furniture made with oak will last a lifetime (or longer).
If price dictates your decision, that's fine (it factors in for just about all of us), but I think I would paint pine before staining it. We also have lots of white trim, so occasionally we use pine and paint it white (great for moldings, bookshelves, and other misc things).
Wade