The first is Simon Bernfield's Toledot Shir. It seems like a somewhat mass-produced volume (part of a series of such Toldot by Dr. Bernfeld). Bernfeld was writing at at time when the image of the enlightened Maskil (i.e. rationalists) had lost its glamour and the more mystical, romantic type was becoming in vogue. Bernfeld tries rather too hard to seem objective, constantly declaiming that "he has now wish to act as Shir's "defender"" which gives the book a very jumpy feeling since he tries to write from four points of view at once.
This style displeased the adherents of the enlightened maskil school. A Feivel Wettstein put out a small pamphlet "L'Toledot Shir" as a scathing (but not very good) attack on Bernfeld and to defend Shir. Bernfelds book does an adequate job sketching the basics of Shir's biography but he hardly takes advantage of the abundance of material, both in print, and still in manuscript nor can we is his analysis particularly perceptive.
The next study shares most of the faults of the former (indeed he appears to have borrowed quite heavily from Bernfelds book). This is Isaac Eisenstein-Barzilay's (Barzilay is the Hebrew for eisen) "Shir and his contemporaries. The first part is an adequate overview of "The Scholarly Contribution of Shelomo Judah Leib Rapoport", first printed as an article in PAAJR (I thank R' S. for notifying me of that article). The second is an overview of Shir's polemics. It is on the whole a very adequate job, and some pieces of his analysis (e.g his analysis of his polemic with Fisher/Hirsch - although even here he misses the point as I hope to show) are quite good but in general it is mostly a summary of the various polemics without much in the way of analysis. He also narrowly focuses on only these two areas leaving many aspects that still need to be explored.