diff --git a/pkgs/stdenv/custom/default.nix b/pkgs/stdenv/custom/default.nix
index 4c7380118f7d5..7f1fe3e404235 100644
--- a/pkgs/stdenv/custom/default.nix
+++ b/pkgs/stdenv/custom/default.nix
@@ -2,7 +2,7 @@
 , localSystem, crossSystem, config, overlays, crossOverlays ? []
 }:
 
-assert crossSystem == localSystem;
+assert lib.systems.equals crossSystem localSystem;
 
 let
   bootStages = import ../. {
diff --git a/pkgs/stdenv/darwin/default.nix b/pkgs/stdenv/darwin/default.nix
index a83f727cfe17c..a51e7622d5357 100644
--- a/pkgs/stdenv/darwin/default.nix
+++ b/pkgs/stdenv/darwin/default.nix
@@ -36,7 +36,7 @@
     }
 }:
 
-assert crossSystem == localSystem;
+assert lib.systems.equals crossSystem localSystem;
 
 let
   inherit (localSystem) system;
diff --git a/pkgs/stdenv/default.nix b/pkgs/stdenv/default.nix
index 7a2ad665e09d7..bc61a2ab174d9 100644
--- a/pkgs/stdenv/default.nix
+++ b/pkgs/stdenv/default.nix
@@ -36,7 +36,7 @@ let
 
   # Select the appropriate stages for the platform `system'.
 in
-  if crossSystem != localSystem || crossOverlays != [] then stagesCross
+  if !lib.systems.equals crossSystem localSystem || crossOverlays != [] then stagesCross
   else if config ? replaceStdenv then stagesCustom
   else if localSystem.isLinux then stagesLinux
   else if localSystem.isDarwin then stagesDarwin
diff --git a/pkgs/stdenv/freebsd/default.nix b/pkgs/stdenv/freebsd/default.nix
index de66085876052..c284c9b8948ef 100644
--- a/pkgs/stdenv/freebsd/default.nix
+++ b/pkgs/stdenv/freebsd/default.nix
@@ -2,7 +2,7 @@
 , localSystem, crossSystem, config, overlays, crossOverlays ? []
 }:
 
-assert crossSystem == localSystem;
+assert lib.systems.equals crossSystem localSystem;
 let inherit (localSystem) system;
     fetchURL = import <nix/fetchurl.nix>;
     trivialBuilder = (import ./trivial-builder.nix);
diff --git a/pkgs/stdenv/linux/default.nix b/pkgs/stdenv/linux/default.nix
index 9cfe21e3640d4..fb0bc94ad4ca3 100644
--- a/pkgs/stdenv/linux/default.nix
+++ b/pkgs/stdenv/linux/default.nix
@@ -95,7 +95,7 @@
   in files
 }:
 
-assert crossSystem == localSystem;
+assert lib.systems.equals crossSystem localSystem;
 
 let
   inherit (localSystem) system;
diff --git a/pkgs/stdenv/native/default.nix b/pkgs/stdenv/native/default.nix
index bae4ff2c93b26..38ff1f9c3bcdc 100644
--- a/pkgs/stdenv/native/default.nix
+++ b/pkgs/stdenv/native/default.nix
@@ -2,7 +2,7 @@
 , localSystem, crossSystem, config, overlays, crossOverlays ? []
 }:
 
-assert crossSystem == localSystem;
+assert lib.systems.equals crossSystem localSystem;
 
 let
   inherit (localSystem) system;
diff --git a/pkgs/stdenv/nix/default.nix b/pkgs/stdenv/nix/default.nix
index e9e9936ccd801..7089fb8f1bb56 100644
--- a/pkgs/stdenv/nix/default.nix
+++ b/pkgs/stdenv/nix/default.nix
@@ -4,7 +4,7 @@
 , ...
 }:
 
-assert crossSystem == localSystem;
+assert lib.systems.equals crossSystem localSystem;
 
 bootStages ++ [
   (prevStage: {
diff --git a/pkgs/top-level/default.nix b/pkgs/top-level/default.nix
index ba00e78ce2e62..addf7b39a8c95 100644
--- a/pkgs/top-level/default.nix
+++ b/pkgs/top-level/default.nix
@@ -60,11 +60,24 @@ in let
 
   localSystem = lib.systems.elaborate args.localSystem;
 
-  # Condition preserves sharing which in turn affects equality.
+  # Condition preserves sharing which in turn improves equality within this Nixpkgs.
+  #
+  # Use `lib.systems.equals` to compare systems.
   crossSystem =
-    if crossSystem0 == null || crossSystem0 == args.localSystem
-    then localSystem
-    else lib.systems.elaborate crossSystem0;
+    if crossSystem0 == null || lib.systems.equals crossSystem0 args.localSystem
+    then
+      # This makes `crossSystem == localSystem` so that comparisons with `==`
+      # work **in the context of this single Nixpkgs invocation**.
+      #
+      # Equality is still broken when comparing between two Nixpkgs instances:
+      #
+      #      (import <nixpkgs> {}).stdenv.hostPlatform
+      #   != (import <nixpkgs> {}).stdenv.hostPlatform
+      localSystem
+    else
+      # It's a truly different system, so no significant equality problems.
+      # We only have to elaborate it, just like we did for localSystem above.
+      lib.systems.elaborate crossSystem0;
 
   # Allow both:
   # { /* the config */ } and