Lens advise for Nikon D40x?

I want to buy a lens for my Nikon D40x. I'm currently using the kit lens (55-200mm).
I have shortlisted the following two lenses -
1. 55-200 mm
2. 55-300mm
Both are by Nikon.
Please tell me which one is better, and also if there's some other lens, better than this one, in the same price range as these lenses.

these are my pics, if you would like to see what kind of work i'm interested in.

Better is a relative term.

If you need the extended reach of the 55-300 mm, then it is a better choice.

If not, the 55-200 is just fine

I assume you did a typo there. The kit lens is 18-55mm. There's no better lens per se. It will all depend on what you need. Do you want to go further? The 55-300mm will be better.