SHAKE-128/256 or SHA3-256/512 Would it be better to use SHAKE-128/256 or SHA3-256/512? In what situation should I chose one over the other?
And in which case would it be more interesting to use one or another?


So SHA3-$n$ offers $n$ bits of security against preimage and second-preimage attacks and $n/2$ bits of security against collision attacks.
On the other side SHAKE-$n$ offers at $n$ bits of security against preimage and second-preimage attacks and also $n$ bits of security against collision attacks (assuming the digest is at least $2n$ bits long). So when to use which?


When you are forced to use "an approved hash function", you use SHA3, because SHAKE doesn't qualify.
When you need a really long hash output (or an XOF in general), you use SHAKE.
When you really need more than 256 bits of security against preimage or second-preimage attacks you use SHA3.
When you want to be compatible with more other systems, you probably want to use SHA3.
When speed matters to you (and you still want to use SHA3 / SHAKE) and you are happy with an all-arond $n$-bit security level (for $n\in\{128,256\}$), you use SHAKE.


This last point follows from the fact that the higher preimage resistance in SHA3 is paid for with lower rate (=number of new bits processed per internal permutation invocation) which is usually higher in SHAKE than in SHA3 (SHAKE256 has the same as SHA3-256).