The biggest difference is that Ant will ensure that dependencies declared via depends are called at most once. For example:
<target name="a" />
<target name="b" depends="a" />
<target name="c" depends="a" />
<target name="d" depends="b, c" />
If I call target d, b and c are called. However, a is only called once (even though both b and c depends on it).
Now suppose we decide to use antcall instead of depends for target d:
<target name="d">
<antcall target="b" />
<antcall target="c" />
</target>
Calling target d will now call targets b and c; however, target a will get called twice, once for b and then again for c.
In other words, antcall sidesteps the normal dependency rules that are the cornerstone of Ant.
I don’t think antcall should be used as a substitute for normal Ant-like dependencies; that’s what depends is for. So when would you use it? The antcall task does allow you to control what properties and references are defined (which is why a new Ant environment is created–and why it’s so slow) so it can be used to create variants of the same thing; e.g., maybe two jars, one with and one without debug symbols.
Overusing antcall, however, creates slow, brittle, and hard to maintain build scripts. Think of it as the goto of Ant–it’s evil. Most well-written build scripts simply don’t need it except in unusual cases.