剧烈 and 激烈
jùliè and jīliè

Both words mean "to be fierce, violent."
1. When applied to injury or wound, 剧烈 and not 激烈 is used.
(1) 当时，她突然感到腹部一阵剧烈的疼痛。
Dāng shí, tā tū rán gǎn dào fù bù yí zhèn jù liè de téng tòng.
She suddenly got a stomachache.

(2) 剧烈的疼痛令他说不出话来。
Jù liè de téng tòng lìng tā shuō bù chū huà lái.
A violent pain left him speechless.

2. When applied to thought, speech, sentiments, etc. 激烈 and not 剧烈 is used.
(1) 经过一番激烈的辩论，他终于认同了对方的观点。
Jīng guò yì fān jī liè de biàn lùn, tā zhōng yú rèn tóng le duì fāng de guān diǎn.
After the argument he finally understood the opposite point of view.

(2) 双方当时的言辞太过激烈，最终演变成为打架事。
Shuāng fāng dāng shí de yán cí tài guò jī liè, zuì zhōng yǎn biàn chéng wéi dǎ jià shì jiàn.
Both sides said things they didn't mean, and it finally led to a fight.

3. When applied to completion, etc. 激烈 is usually used.
(1) 这场比赛进行得十分激烈。
Zhè chǎng bǐ sài jìn xíng de shí fēn jī liè.
This game is very intense.

(2) 当食物变得稀缺时，种群之间的斗争往往会更加激烈。
Dāng shí wù biàn de xī quē shí, zhǒng qún zhī jiān de dòu zhēng wǎng wǎng huì gèng jiā jī liè.
When food becomes scarce the struggle amongst a species becomes more intense.

4. When applied to undulation of thoughts, either word will do.
(1) 在一番激烈 (剧烈) 的思想斗争之后, 他退出比赛。
Zài yì fān jī liè (jù liè) de sī xiǎng dòu zhēng zhī hòu, tā tuì chū bǐ sài.
After after anguishing over it, he finally forfeited the match.

5. When qualifying a beat, shake, or change, 剧烈 is used.
(1) 汽车剧烈地颠簸起来，可想而知车里的人有多难受。
Qì chē jù liè de diān bǒ qǐ lái，kě xiǎng ér zhī chē,lǐ de rén yǒu duō nán shòu.
This car doesn't ride very nice when we go over bumps.

(2) 随着气氛的紧张，他的心跳剧烈地动起来。
Suí zhe qì fēn de jǐn zhāng, tā de xīn jù liè de tiào dòng qǐ lái.
The intense atmosphere made his heart beat faster.

(3) 股市随时可能发生剧烈的变化。
Gǔ shì suí shí kě néng fās hēng jù liè de biàn huà.
The stock market can have dramatic changes at any time.

两个词都可表示厉害，猛烈。
1.用于身体伤痛时，用"剧烈“而不用"激烈。”
2.用于思想，言论，情绪等，用“激烈”不用“剧烈。”
3.用于竞赛，竞争等，多用“激烈。”
4.用于思想起伏，两个词都可以用。
5.用于跳动、振动、变动，用“ 剧烈。”