Are there biochemical differences between the cell membranes of prokaryotes and eukaryotes?
There are differences. (Except mitochondrial eukaryotic membranes, which are indeed similar to bacterial membranes! (reviewed in van Meer et al., 2008)). 

First, bare in mind that it is thought that even different eukaryotes, such as Fungi and Humans, have different cell membrane compositions and that this is reflected in the proteins (Sharpe et al, 2010). The outer membrane of Gram negative bacteria isn't even made of phospholipids, it's made of glycolipids (Kamio &amp; Nikaido, 1976). Archean membranes have the most notable lipid compositions, including a bilayer-like monolayer, to adapt to the conditions they are found in (Oger et al 2013). My point being that saying "there are differences" is indeed an understatement.

This question has probably arisen because anti-microbial peptides seem to act with specificity, and that perhaps this specificity comes from direct peptide-lipid interaction. This is on the right lines. From wikipedia:


  The cell membranes of bacteria are rich in acidic phospholipids, such as phosphatidylglycerol and cardiolipin[23][27]. These phospholipid headgroups are heavily negatively charged. Therefore, the outmost leaflets of the bilayer which is exposed to the outside of the bacterial membranes are more attractive to the attack of the positively charged antimicrobial peptides. 


Notably, no such charge exists in eukaryotes since the negative charge is found on the inner leaflet of the plasma-membrane rather than the outer leaflet.

There is such a massive variation, even within bacterial membrane composition (Bogdanov et al 2014), that I cannot even really begin to list it here. Furthermore, there are variations in the glycocalyx, surface proteins, and lipid composition dynamics due to lipid rafts.