...的 are different.
As you have already known,
...的 can construct adjective clause.
(subject + verb) + 的 + noun = noun + which + subject + verb
And in Chinese, the noun can be omitted in a clear context. In this case,
……的 constructs a noun clause.
我喜欢的（人）是你。 Who I like is you.
(subject + verb) + 的 = what/who + subject + verb
Though it's not so obvious, the function of 所 in
所 is put before a verb, corresponding to the previous
被, indicating passive voice. (And
为/被 is often omitted.)
Unfortunately, many chinese verbs are either transitive or intransitive, so the sentences containing
所...的 often look alike.
我爱的人 the person who I love
(被)我所爱的人 [literal translation] the person who is loved by me
我讨厌的是你。 Who I hate is you.
我所讨厌的是你。 [literal translation] (The person) who is hated by me is you.
Difference between them
Thus, the difference between the two structures is whether it is passive voice or not. In most cases, one can be reconstructed to another.
Q: So, which one should I use in the xxx case?
A: It depends on personal choice. Just as you didn't said which one should be used (by me) in the xxx case?
EDIT: Some irreplaceable examples
There is preference in some situations. Some idioms can only be expressed in a unique voice (active or passive). Though this meaning of 所
4. 用在动词前，代表接受动作的事物 is listed as a single entry, in the grammar structure, it's actually the passive voice. So I include it in the passive-only case.
(Right) 天杀 的 政府 the goddamn government = [literal translation] the government which god should kill
(Wrong) 天 所 杀 的 政府
(Right) 狗日 的 政府 the fxxking government = [literal translation] the government which dogs should fxxk
(Wrong) 狗 所 日 的 政府
(Right) 你 所 谓 的 正义 your so-called justice = [literal translation] the justice which is called (only) by you
(Wrong) 你谓 的 正义
谓 is a special verb, so in the example above (well, I don't mean everywhere), it can only be in the passive voice. However, a character with the same meaning,
说, can be in either active or passive voice.
你所说的正义 are OK.
Anyway, idioms always need to be memorized mechanically. It's difficult to find an easy rule for them.