There is a significant time difference between methods 1 and 2 which is presumably because of the inner loop encoded explicitly in perl in method (2) vs the implicit inner loop in method (1) actually implemented in C.

use feature ":5.14";
use warnings FATAL => qw(all);
use strict;
use Time::HiRes qw(time);
use Data::Dump qw(dump pp);

my %checkFrom;
my @toCheck;

sub init0()
 {@toCheck = (); 
  push @toCheck, rand(1e6) for 1..1e4;
 }

sub init1()
 {%checkFrom = ();
  for   my $x(0..999)
   {for my $y(0..999)
     {$checkFrom{$x}[$y] = 1e3*$x+$y;
     }
   }
  init0();
 }

sub init2()
 {%checkFrom = ();
  for   my $x(0..999)
   {for my $y(0..999)
     {$checkFrom{$x}{$y} = 1e3*$x+$y;
     }
   }
  init0();
 }

for(1..10)
 {if (1)
   {init1();
    my $s = time();
     {my %toCheck = map { $_ => 1 } @toCheck;
      @$_ = grep !$toCheck{$_}, @$_ for values %checkFrom;
     } 
    say "1 took ", (time() - $s);
   }

  if (2)
   {init2();
    my $s = time();
     {for my $thing (@toCheck)
       {for my $category (keys %checkFrom)
         {delete $checkFrom{$category}{$thing};
         }
       }
     }
    say "2 took ", (time() - $s);
   }
 }
[download]

Produces

1 took 1.06206107139587
2 took 11.8416769504547
1 took 1.10106301307678
2 took 12.3792278766632
1 took 1.07640194892883
2 took 12.4490790367126
1 took 1.2350709438324
2 took 12.7647299766541
1 took 1.27407312393188
2 took 12.8677358627319
1 took 1.17906808853149
2 took 12.6504328250885
1 took 1.17000198364258
2 took 12.8158860206604
1 took 1.2890739440918
2 took 12.8577361106873
1 took 1.32807612419128
2 took 12.7377278804779
1 took 1.24107122421265
2 took 12.7136778831482