Best Professional Video editor for Linux equivalent to Sony Vegas Pro?

Try Cinelerra.

Cinelerra is the most advanced non-linear video editor and compositor for Linux. Cinelerra also includes a video compositing engine, allowing the user to perform common compositing operations such as keying and mattes.^Cinelerra

To download click here. (Edit: or install on 12.04 with the following commands.)

sudo apt-add-repository ppa:cinelerra-ppa/ppa
sudo apt-get update
sudo apt-get install cinelerra-cv

Also you can try OpenShot.

OpenShot has many great features, such as trimming and arranging videos, adjusting audio levels, transitions between videos, compositing multiple layers of video, chroma-key / green screen effect, and support of most formats and codecs.

What really sets OpenShot apart from other video editors is the easy-to-use user interface.^OpenShot

To install OpenShot, just press Ctrl+Alt+T on your keyboard to open Terminal. When it opens, run the command(s) below:

sudo add-apt-repository ppa:openshot.developers/ppa
sudo apt-get update
sudo apt-get install openshot openshot-doc

Kdenlive

One of most Fascinating application can be found on Ubuntu for Free.

It can do all most all the Functions that can commercially available famous applications do.

Input and output with many formats.

Can create Creative Overlays including Titles, Headers etc.

Have many functions for Tracks.

Many video and audio Effects and Transitions.

Can Do Video capture using External Camera, Webcam or Screen Capture.

You can also install in Terminal with:

sudo apt-get install kdenlive kdenlive-data

You can also try Lightworks.

Another great option is Blender. Here is a good Video Sequence Editor Tutorial.