The big difference between the tone/base curve and the tone equalizer is that the former are tonal adjustments, while the latter is a spacial change.
The curves affect all pixels of a particular brightness the very same way. The equalizer segments the image into areas, then changes exposure smoothly in these areas.
Say you reduced highlights and lifted shadows. With the curve, this will reduce contrast in every part of the image. With the EQ, contrast within each region will remain unchanged, but the overall dynamic range is reduced. This looks more natural in most images.
The downside is, the tone EQ can produce subtle halos if pushed too far. Look for them in the little preview at the top left of the screen. They can be hard to spot in the full-screen view. (And the halos are much better-behaved than e.g. Lightroom’s Shadows and Highlights slider).