2

Both mean "victory" so I would like to know when is it more convenient to use 勝ち, and when shoud I use 勝利 ?

Is one of them more polite ?

4

The difference is that one of the two is originally Japanese and the other has been loaned from Chinese. We have a million word pairs like that if you did not know it.

「勝{か}ち」 is an originally Japanese word as I hope you could tell from its sounds/reading.

「勝利{しょうり}」 is a Sino-loanword.

The big rule of thumb is that in such word pairs, the Sino-loanword is usually more formal, technical, academic, etc. than the more intuitive original Japanese word. 勝利 vs. 勝ち is no exception. 勝利 sounds more formal than 勝ち.

Is one of them more polite ?

No, this has nothing to do with politeness. 「勝利」 simply is a "bigger" word than 「勝ち」 just as "profound" is a bigger word than "deep" for English-speakers.  

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