"不客气" (bù kèqì) vs "谢谢你" (xièxiè nǐ)
Stepping in for my Chinese to Australian translations:
Also a couple of other phrases that are good to keep in your toolkit

Thank you



谢谢 Xièxiè

Is the most basic and common way of saying thank you
Australian Translation:
Cheers
Thanks

谢谢你 Xièxiè nǐ

This is a more sincere or formal way of saying thank you
Australian Translation:
Thank you
Thanks Heaps

多​谢 Duōxiè

Translates to many thanks, Where 谢谢你 Xièxiè nǐ is used to more formally express a greater amount of thanks 多​谢 Duōxiè is a slightly more casual way of saying the same.
Australian Translation:
Cheers mate this helped a ton
Thanks, I really appreciate this

我​很​感​谢​ Wǒ hěn gǎnxiè

Translates to I am very thankful/Grateful. This term I'm less familiar with but to me it would be to a way of expressing a large amount of gratitude in a formal manner. Same sort of situations 您 Nín is used over 你 Nǐ
Australian Translation:
Thank you sir, I appreciate this.  

Responses



不客气 Bù kèqì

The best translation for this is No politeness necessary or more commonly You're welcome
Australian Translation:
You're welcome

不用谢 Bùyòng xiè

It literately means "No need thanks"
Australian Translation:
Don't worry about it mate

没事 Méishì

It literally translates to "Nothing Thing" but a more natural translation would be it's nothing / never mind 
Australian Translation:
It was nothing mate (As in it was no trouble)



Post thoughts

Responding to 谢谢 (xièxiè) with 谢谢你 (xièxiè nǐ) although would be understood it isn't a way I have heard before. I think it would work well if someone who you were in a position to thank thanked you before you said thank you. An example would be purchasing something from someone as you're both equally profiting from the interaction but if the thanks are one sided I wouldn't use 谢谢你

I mean if you helped a lady up after she tripped and then thanked her for letting you help her she would scream 变态 (biàntài) and slap you across the face assuming you took some sick joy in it



Bonus way of saying thanks

note: this is not about the Chinese language but the Chinese culture

When someone pours you a cup of tea rather then vocalizing your thanks you can tap 2 fingers on the table.


  This custom is said to have originated in the Qing Dynasty when Emperor Qian Long would travel in disguise through the empire. Servants were told not to reveal their master's identity. One day in a restaurant, the emperor, after pouring himself a cup of tea, filled a servant's cup as well. To that servant it was a huge honour to have the emperor pour him a cup of tea. Out of reflex he wanted to kneel and express his thanks. He could not kneel and kowtow to the emperor since that would reveal the emperor's identity so he bent his fingers on the table to express his gratitude and respect to the emperor.    


-Partial Extract from Wikipedia