I have two expression matrices (normalized, using dChip), with the same data except that in one of them , the expression values are log-transformed. I am trying to perform WGCNA analysis on them and getting different plots for scale independence.

First image: For the log-transformed values, some of the power-values (like 9,10) seems to approach 0.9 (red line corresponds to0.9).

Second image: For the plot in which the data is not log-transformed, none of the power-values are falling beyond R^2>=0.9, (the red line corresponds to0.8). I am in a dilemma as to which beta threshold I should consider and whether one should take log-transformed values or not for the analysis

In general, for microarray expression, you will want to log-transform the data before proceeding. A lot of methodologies make implicit assumptions of "normality" that will hold approximately for log-transformed data but will not for linear-scale expression values.

thank you so much for the insight..i was really confused regarding this

Which log transform should we apply? log2?