You are not comparing apples to apples. You map loop assigns (copies) the entire array in addition to incrementing each element. If you drop the assignment, map beats foreach.
My results
foreach(@a){$_+=1;};
real 0m4.941s
user 0m1.096s
sys 0m3.604s
-----------------------
@a = map{$_+= 1} @a;
real 0m6.248s
user 0m2.652s
sys 0m2.900s
------------------------
map{$_+= 1} @a;
real 0m3.224s
user 0m2.908s
sys 0m0.232s
Note: It is generally considered poor form to use map only for its side effects.
Updated to clean up and add note
Update 2: More rigorous timing show that foreach is indeed faster --> Re^3: map vs for\foreach.
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