The suggestion to use proportionality is probably the correct one if you are interested in similar patterns between samples. But not if you are interested in absolute differences.
For example: the following two samples are similar in pattern, but not similar on absolute levels:
Sample 1 Sample 2 Sample 3
Gene A 10 100 80
Gene B 8 80 100
Gene C 12 120 120
Samples 1 and 2 have a perfect proportionality (phi is 0) and also a perfect correlation (as a side note any pair with a perfect proportionality will always have a perfect correlation). However, in terms of logfold changes, samples 2 and 3 are more like each other.
Of course in real life you would never see a comparison like the sample 1 - sample 2 one because normalisation would have removed the scale difference. This was exactly the point brought up by the proportionality paper. But normalisation methods don't normally guarantee that the sum of expression for each sample is identical, and such differences can still occur.
An alternative that might suit more in the second case is either the euclidean distance between the samples, or the euclidean distance on the first two components of a principle component or multi-dimensional scaling. The latter is effectively using mean logFC between samples.
x is a matrix containing normalised, log transformed expression values, you could use R and limma to calculate distance in multi-dimensional scaled space as follows:
mds <- plotMDS(x, plot=FALSE)
mds <- data.frame(mds$x, mds$y)
distances <- dist(mds)