I since discovered that both versions add a scope.
Yes, but they aren't the same scopes. The EXPR variant doesn't create a lexical scope; the BLOCK variant does: 
$ perl -Mstrict -wcE 'my @x = map my $x = $_, 2; say $x'
-e syntax OK
$ perl -Mstrict -wcE 'my @x = map {my $x = $_} 2; say $x'
Global symbol "$x" requires explicit package name at -e line 1.
-e had compilation errors.

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I'm not quite sure what kind of scoping effects happen. 
$ perl -Mstrict -wE 'my @x = map my $x = $_, 2; say $x'
Use of uninitialized value $x in say at -e line 1.
$ perl -Mstrict -wE 'my $x; my @x = map $x = $_, 2; say $x'
2

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So, if we declare $x in the first argument of map, $x exists afterwards, but doesn't have a defined value. If declared before the map, it keeps the last assigned value.

I guess that's more an artifact of the implementation than that it was designed to work this way.

In reply to Re^2: syntax of map operator by JavaFan
in thread syntax of map operator by sman

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