What are the advantages and disadvantages of mapping to genome or transcriptome? Is there a good quality transcriptome available for Macaca Mulata and human?

The advantage of mapping to transcriptome is definitely the time, it takes more time to map reads to the genome. I also head that for some species a good quality transcriptome is not available so it is preferred to map to genome and the other way round. I could not find any comparison paper where the same reads were mapped to genome and transcriptome.

I found the same questions on SeqAnswers, though they out of date (year 2010 and 2014).
It depends on what your interest is. 

If you are happy with the transcriptomes available then you can use them with following caveats (besides points you already mention above): A. you are not going to be able to identify new transcripts B. there is some chance that reads may align in regions that they may not have originated from. On plus side: you can use programs like `salmon` (that don't need to align the data) to  speed the process up while requiring significantly less hardware resources. Using `salmon` with `genome decoys` will help avoid stray matches (ref: https://www.biostars.org/p/456231/#456366 ).

Human transcriptome is reasonably well characterized at this time. If you are not interested in alternately spliced transcripts then there is `RefSeq select` and `MANE` ([**LINK**][1]) datasets that you can use. I am not sure what the status is for Macaca. 


  [1]: https://www.ncbi.nlm.nih.gov/refseq/MANE/