Fine control over the font size in Seaborn plots for academic papers

You are right. This is a badly documented issue. But you can change the font size parameter (by opposition to font scale) directly after building the plot. Check the following example:

import seaborn as sns
tips = sns.load_dataset("tips")

b = sns.boxplot(x=tips["total_bill"])
b.axes.set_title("Title",fontsize=50)
b.set_xlabel("X Label",fontsize=30)
b.set_ylabel("Y Label",fontsize=20)
b.tick_params(labelsize=5)
sns.plt.show()

, which results in this:

To make it consistent in between plots I think you just need to make sure the DPI is the same. By the way it' also a possibility to customize a bit the rc dictionaries since "font.size" parameter exists but I'm not too sure how to do that.

NOTE: And also I don't really understand why they changed the name of the font size variables for axis labels and ticks. Seems a bit un-intuitive.

It is all but satisfying, isn't it? The easiest way I have found to specify when setting the context, e.g.:

sns.set_context("paper", rc={"font.size":8,"axes.titlesize":8,"axes.labelsize":5})   

This should take care of 90% of standard plotting usage. If you want ticklabels smaller than axes labels, set the 'axes.labelsize' to the smaller (ticklabel) value and specify axis labels (or other custom elements) manually, e.g.:

axs.set_ylabel('mylabel',size=6)

you could define it as a function and load it in your scripts so you don't have to remember your standard numbers, or call it every time.

def set_pubfig:
    sns.set_context("paper", rc={"font.size":8,"axes.titlesize":8,"axes.labelsize":5})   

Of course you can use configuration files, but I guess the whole idea is to have a simple, straightforward method, which is why the above works well.

Note: If you specify these numbers, specifying font_scale in sns.set_context is ignored for all specified font elements, even if you set it.