きつい implies difficulty, in the physical, logical, or opinionated realms
つらい implies difficulty in the emotional or interpersonal relationship realms
For the 仕事 example
仕事がつらい means that work is difficult to the point of physical and mental distress or pain.
On the other hand,
仕事がきつい means that work's definitely not easy, and some serious effort is required, but it still hasn't reached the threshold of "I can't do this anymore".
Examples of きつい
(based on https://dictionary.goo.ne.jp/jn/52804/meaning/m0u/)
- Harsh sunlight or a strong scent can be きつい
- The taste of something, or a food/drink can be きつい
- The application of force can be きつい if it's too strong.
- A garment that's too tight is きつい
- A rule or request can be きつい
- Work can be きつい if it's really difficult to do well.
- Someone's personality can be きつい
See https://dictionary.goo.ne.jp/word/en/%E3%81%8D%E3%81%A4%E3%81%84/ for a bunch of English examples
Examples of つらい
(based on https://dictionary.goo.ne.jp/jn/148479/meaning/m0u/)
- a person being "cold" to someone else is つらい
- Work or practice is つらい if it's very mentally and physically taxing or stressful
- something is つらい if it's problematic and difficult to deal with
- someone is つらい if he/she is inconsiderate of another's feelings
- someone is つらい if he/she is irritating
See https://dictionary.goo.ne.jp/word/en/%E8%BE%9B%E3%81%84/#je-50515 for a bunch of English examples (includes 辛い as からい as well)