I'm going to use it for street photography, portraits and landscapes.

My "Every Day Carry" camera is the Fuji X10. It never leaves my side.

I take way more personal pictures with it than my DSLR and it rarely disappoints.

You might feel a bit limited by the X10's lens range, it's slightly conservative 28-112mm takes care not to sacrifice optical quality by over stretching itself; a compromise I feel that's worthy of the robust design and quality aesthetic this retro camera embodies.

(A DSLR's is great if you're "serious" about photography. You will learn more about camera controls from a DSLR, provided you're bold enough to switch it out of program or "scene" modes.  A DSLR is the camera to take on a photography course, to camera clubs, to wave about like a pro and to covet expensive lenses and accessories for)

However my expensive DSLR stays mostly at home when I go out to play.

Totally different cameras, so I can't recommend until I know what you plan to use them for. I currently have an EOS 5D mk 2 and the Fuji x10 for when I don't want to take my DSLR with me. However my first DSLR was a canon 1000d so I think I can compare them well. 

There's no question the DSLR will take better photos, it has a much bigger sensor and will focus and shoot much quicker. The flexibility you get with interchangable lenses and the amount of true control can't yet be matched by a compact camera. 

If you are just starting to learn about photography, you'll learn much more by starting with a DSLR. 

The downside to a DSLR is of course that it is much bulkier, and certainly there are times when I don't want to take my kit with me. I bought the Fuji because I wanted a high performance compact, and it does pretty well. 

It shoots in RAW (an uncompressed image file) which means you have much more control when processing, shoots fast (10 frames per second) and notionally gives you similar settings to a DSLR. In reality, it is just much slower to use - once you get used to the responsiveness of a DSLR, it's hard to get used to even a good compact. It also struggles in low light. 

Bottom line, if you want the best image quality, or want to learn about photography, get the DSLR. If size is a critical factor, or you just want better shots than a cheaper point and shoot, the Fuji is a good choice. 

Much more solid build, Much MUCH more discreet, more portable (as its lighter) and the lens is fantastic.