DSLR or fixed-lens digital camera?

I've been considering either the Nikon D5100, or Fujifilm Finepix HS20,
the photo quality on both seemed nice, and while it would be nice to have interchangeable lenses, cost is also a factor? Ideas?

What do you want to do with your photography?

Take control and produce high quality images, you will need a dSLR and the D5100 is an excellent one.

The Fujifilm HS20 takes the control from you and has a sensor that is over 15 time smaller, thus lower possible quality, once you develop the skills using a fully adjustable camera like the D5100

When you open the box of your DSLR, you begin a creative journey, guided by your vision and bound only by your budget and how quickly you acquire new skills. You can choose lens and accessories to capture action, remember vast landscapes, reveal new-found visions, or preserve the beauty of those you love.

When you open the box of a point & shoot or bridge camera, you have a nice camera. Period.

If you desire room to grow, get a the D5100. If you just want instant gratification, then get the HS20.

Get the point and shoot only if you absolutely can't afford even the entry level d3100, point and shoots look like web cams compared to the d5100 or d3100 our even the entry canon t3