Kanji is the Japanese word for 漢字 (Chinese character). It is "hanzi" in Chinese. And only hanzi has tranditional and simplified forms. Kanji is also simplified, but kanji has only one official form in Japan.
Chinese Simplified is the official writing system in mainland China, Chinese Traditional is the official writing system in Macau, Hong Kong, Taiwan. Mainland China also use Chinese Traditional in some special situation, for example, in calligraphy, in trademarks.
Not all traditional Chinese characters are simplified, so some simplified Chinese characters are identical to their traditional counterparts, for example, 更(simplified) and 更 (traditional).
Some are slightly different, for example, 强(simplified) and 強(traditional).
Some are very different, for example, 龙(simplified) and 龍(traditional).
As I just said, traditional Chinese characters are still used in mainland China for calligraphy. That's because many traditional Chinese characters look more balanced in structure than their simplified form.
Here is some example:
So if you want to use Chinese characters for tattoo, I would suggest traditional Chinese characters, because they are more balanced in structure and more good-looking.
Coincidentally, the simplified version of the "愈挫愈勇" suggested by @bfrguci is identical to their traditional counterparts.
@sazarando suggests grass script for tattoo. I'd like to remind you that Chinese characters written in grass script is hard to recognize even for native speakers of Chinese language, so I personally don't think it a good choice. I suggest you choose from clerical script, regular script, semi-cursive script. All these three scripts are widely used for handwritten Chinese characters, both simplified and traditional, in China, Taiwan, Hong Kong and Macau. But just as @sazarando said, avoid fonts for print if you could.
@greglow give a an article comparing traditional and simplified Chinese. I skimmed through this article and found some of its arguments very controversial and misleading. I'll explain what I mean in detail.
1, "The traditional Chinese, most of them are hieroglyphic. It conveys more significant than simplified Chinese." This is incorrect. You can refer to Chinese character classification in Wikipedia. Chinese characters are roughly classified into six categories based on the rules they are formed, that is, pictographs, simple ideograph, compound ideographs, phono-semantic compounds, rebus, transformed cognates. There is no accurate number, but it's estimated that about 90% of Chinese characters, traditional or simplified, are phono-semantic compounds. Pictographs, or hieroglyphic, comprise only 4% of all Chinese characters. That's because pictograph is only suitable for concrete things, for example, sun (日), moon (月), eye (目), mountain (山), rain (雨), elephant (象) and so on. It's hard to depict abstract concepts using only pictographs, in which case the other five formation rules come into play.
2, The article gave some examples to demonstrate that "traditional Chinese character conveys more significant than simplified Chinese". But the examples it used are not very persuasive. It claimed 愛 (traditional) is better than 爱(simplified, means love) because 愛 (traditional) has a 心(heart) as its component so it conveys the meaning that we love with heart. But I can also argue that 爱(simplified) is better because it has a 友 (friend) in the mid of the word, so it convey a broader feeling of love than 愛 (traditional). I can even give some other examples in favor of simplified Chinese. I argue that 党 (simplified, means party as in Democratic Party) is better than 黨 (traditional), because 党 contains a 兄(brother) while 黨 a 黑 (black), so 党 conveys that our Party love its members as brothers and no dirty(black) politics. It's obvious that this kind of arguments is too far-fetched, and it just remind me of something like astrology.
3, "After characters simplified, lots of Chinese people cannot read the ancient classical literature." This is incorrect. In fact, an average literate people in mainland China can read both simplified and traditional Chinese characters without any difficulty, because traditional Chinese characters are still very common in everyday lives. In mainland China, traditional Chinese characters are not banned. Instead, they are allowed to be used for some special situations. According to 《中华人民共和国国家通用语言文字法(Law of the People's Republic of China on the Standard Spoken and Written Chinese Language)》, Chinese government, educational organizations, public service organizations, public TV and broadcasting should use standard(simplified) Chinese characters. And according to Article 17, there are six situations in which traditional Chinese characters can be used publicly and lawfully:
Article 17: traditional Chinese characters and other variant Chinese characters can be preserved or used in the following situations:
(1) cultural relics and historical sites
(2) in family name
(3) art works, such as calligraphy and seal carving
(4) handwritten characters used in dedication and signboard
(5) if there is necessity to use traditional Chinese characters for publishing, teaching, researching.
(6) some other special situations approved by relevant department of State Council of the People's Republic of China.
At the same time, almost all official dictionary of Chinese characters give both simplified and traditional form of a character. Usually the the traditional form of a character is placed in a pair of parentheses immediately after the simplified form. Here is an example from 《新华字典，第11版 (Xinhua Dictionary, 11th Edition (Chinese Edition)》
, the best-selling and most widely used Chinese dictionary in China.
You can see that both 爱(simplified) and 愛 (traditional) are given out, and the traditional form 愛 is placed in parentheses immediately after the simplified form 爱.
An inscription in traditional Chinese at Mount Tai. 五嶽獨尊 (simplified version: 五岳独尊) and 昂頭天外 (simplified version: 昂头天外). An average literate person in mainland China can read it without any difficulty.
Maybe the most famous calligraphy work in China, Lantingji Xu(simplified Chinese: 兰亭集序; traditional Chinese: 蘭亭集序). It's written in semi-cursive script. Again, an average literate person in mainland China can read it without any difficulty.
The four red characters in the upper-left corner is the name of Xinhua Daily written in traditional Chinese characters. 新華日報(simplified version: 新华日报)
A grandpa exercising his calligraphy at some park in mainland China. This is a kind of outdoor recreation popular among the elderly (thought mainly male) in mainland China. He is writing traditional Chinese characters.