Why is methyl parathion less toxic than ethyl parathion?
Both methyl parathion (O,O-Dimethyl O-(4-nitrophenyl) phosphorothioate) and ethyl parathion (O,O-Diethyl O-(4-nitrophenyl) phosphorothioate) are organothiophosphates with identical structure except for dimethoxy group in methyl analog has been replaced by diethoxy group in ethyl analog. Both analogs are acetylcholinesterase (AChE) inhibitors, although phosphorothioates ($\ce{P=S}$) are less potent inhibitors compared to corresponding phosphate ($\ce{P=O}$) analogs. The active site of AChE is depicted in following Figure (Ref.1) where acetylcholine (ACh) get hydrolyzed:

The hydrolysis mechanism invoves the $\ce{OH}$ of serine residue and imidazole moiety of histidine residue in the active site as shown. The major inhibition mechanism of all organophosphate esters is involved phosphorylation of the $\ce{OH}$ group of serine residue in the active side. The aging (breakage of the $\ce{O-R}$ ester linkages leaving $\ce{P-O-}$ groups) is followed this phosphorylation making the inhibition irreversible.
Although aging can be visualized by the process of hydrolyzing ester group by water molecule attacking phosphorus atom first, replacing $\ce{R-O-}$ group followed by proton exchange, the literature has shown preferably $\ce{O-R}$ breakage. If that's the case, ethyl breakage is facilitated over methyl breakage just by stability of the resultant products ($\ce{CH3CH2^+}$ vs $\ce{CH3^+}$). Hence, we can conclude that ethyl parathion is more potent than methyl parathion.
An early study of inhibitory activity of various batches of ethyl parathion has revealed that a dithio analog,  O,S-Diethyl O-(4-nitrophenyl) phosphorothioate is much potent inhibitor compared to ethyl parathion (Ref.2). It is possible that this dithio analog is a common contaminate during ethyl parathion sysnthesis. Thus, this factor may contributed to the higher activity of ethyl parathion compared to that of methyl parathion.
It is also worth noting that recent studies on versatility of imidazoles or in reactions with organophosphates (OPs, Ref.3). According to this study, OPs from the $\ce{P=O}$ family, imidazole attacks the phosphorus atom exclusively, making $\ce{P-N}$ bond. With the less reactive $\ce{P=S}$ family, an unusual N-alkylation predominates. Surprisingly, imidazole reacts with methyl parathion exclusively at the aliphatic carbon, whilst for ethyl parathion, imidazole reacts by two pathways: at both the phosphorus and aliphatic carbon, with predominance for the latter:

Since immidazole moiety is present in active site of the AChE, one can suggest the different reactivity of ethyl parathion over methyl parathion with imidazole may play a role in their different activity in inhibition.
References:

Hay Dvir, Israel Silman, Michal Harel, Terrone L. Rosenberry, Joel L. Sussman, “Acetylcholinesterase: from 3D structure to function,” Chemico-biological Interactions 2010, 187(1-3), 10-22 (DOI: 10.1016/j.cbi.2010.01.042).
W. M. Diggle, J. C. Gage, “Cholinesterase inhibition in vitro by OO-diethyl O-p-nitrophenyl thiophosphate (Parathion, E 605),” Biochemical Journal 1951, 49(4), 491-494 (https://doi.org/10.1042/bj0490491).
Valmir B. Silva, Elisa S. Orth, “Are Imidazoles Versatile or Promiscuous in Reactions with Organophosphates? Insights from the Case of Parathion,” J. Braz. Chem. Soc. 2019, 30(10), 2114-2124 (https://doi.org/10.21577/0103-5053.20190084 ).