Vrftjkry

I've got 2 polygon feature classes, one with countries and one with sectors of the countries.
How can I prevent country labels from rendering if I have sector classes overlaping them.
So how can you stop drawing labels over other feature classes, rather then over other feature class labels.

I dont think you can do this dynamically without scripting it yourself (you can ensure labels do not over lap, but that is not quite what you are asking for I think?)

If it is just for cartographic purposes an option would be to copy the label column in the attribute table, select by location all those with overlap and simply delete the labels for those with over lap (i.e. the label would then display blank).

Or you could intersect the geometries, select by attribute the combination you which wish to avoid and delete the label data in those fields.

I think weight of the feature is your option.

You can find that option under label manager > placement properties > conflict analysis
and set up value according to help below. (I don't have english version of ArcMap, but this most accurate names I can provide).

A quick tour of the Labeling toolbar

A quick tour of labeling with the Maplex Label Engine

Help on labels weight, below is piece of it

Some common uses for weights:

Prevents all labels from being placed on a given layer of point/line
features or polygon outlines. Do this by increasing feature weight to
High.

Forces ArcMap to consider alternate positions for labels. Do
this by increasing feature weight to Low or Medium.

Prevents some
labels from being placed on top of some features. Do this by
increasing some feature weights and decreasing some label weights.

If
your data frame has annotation groups or annotation layers with
nontext graphics, specify that labels be placed on top of these
graphics by setting the feature weight for the layers and/or groups to
None.