I am particularly interested in the comparison of the trace formula part of JacquetLanglands. But I found the original text hard to read.

I think that you may like the notes by Ioan Badulescu: see http://wwwmath.univpoitiers.fr/~badulesc/pub/JLtata1.pdf They are a 20 pages modern essentially complete exposition of the proof of JacquetLanglands not only for $Gl_2$ but for higher higher rank linear groups and their inner form as well. 


I suggest Gelbart Lecture notes Arthur trace formula in addition to Gelbart Jacquet (Aakumadula`s reference). Here is a site with references: http://www.charlesli.org/math/trace.html 

