Premiere Pro sequence adds black stripes on both sides of the video
Aj Henderson is right.
Your pixel aspect ratio is different in each video.
You can see that from the pool table, the one on the left is stretched out, while the one on the right is squished, it almost almost like you have 16% black bars on either end of the video on the right. Pixel aspect ratio, anamorphic 1.333. 

2 ways to fix it:

1) Square pixels

If you wish to keep the pixels square
Crop the video (scale in) until the crop lines disappear, but of course you will also crop out some content on the top and bottom of the video

2) Create new sequence

Create a new sequence, I am assuming AVCHD, select 1080p folder and then select the item AVCHD 1080p24 Anamorphic (or the 25 frame one, dont know what video setting your source is at). Also note there is a little tab at the top called settings when creating a new sequence, you can click that to view your pixel aspect ratio.

That should fix the issue.