diff --git a/docs/AllRectorsOverview.md b/docs/AllRectorsOverview.md
index 5a7f11d1740..95139bed5a0 100644
--- a/docs/AllRectorsOverview.md
+++ b/docs/AllRectorsOverview.md
@@ -6054,7 +6054,7 @@ Replace deprecated "assertArraySubset()" method with alternative methods
 
 -        $this->assertArraySubset([
 -           'cache_directory' => 'new_value',
--        ], $checkedArray);
+-        ], $checkedArray, true);
 +        $this->assertArrayHasKey('cache_directory', $checkedArray);
 +        $this->assertSame('new_value', $checkedArray['cache_directory']);
      }
diff --git a/rules/phpunit/src/Rector/MethodCall/ReplaceAssertArraySubsetRector.php b/rules/phpunit/src/Rector/MethodCall/ReplaceAssertArraySubsetRector.php
index d43bb274d27..54c1f144309 100644
--- a/rules/phpunit/src/Rector/MethodCall/ReplaceAssertArraySubsetRector.php
+++ b/rules/phpunit/src/Rector/MethodCall/ReplaceAssertArraySubsetRector.php
@@ -49,7 +49,7 @@ public function test()
 
         $this->assertArraySubset([
            'cache_directory' => 'new_value',
-        ], $checkedArray);
+        ], $checkedArray, true);
     }
 }
 PHP
@@ -176,11 +176,13 @@ private function addKeyAsserts(Node $node): void
      */
     private function addValueAsserts(Node $node): void
     {
+        $assertMethodName = $this->resolveAssertMethodName($node);
+
         foreach ($this->expectedValuesWithKeys as $expectedValueWithKey) {
             $expectedKey = $expectedValueWithKey['key'];
             $expectedValue = $expectedValueWithKey['value'];
 
-            $assertSame = $this->createPHPUnitCallWithName($node, 'assertSame');
+            $assertSame = $this->createPHPUnitCallWithName($node, $assertMethodName);
             $assertSame->args[0] = new Arg($expectedValue);
 
             $arrayDimFetch = new ArrayDimFetch($node->args[1]->value, BuilderHelpers::normalizeValue($expectedKey));
@@ -189,4 +191,18 @@ private function addValueAsserts(Node $node): void
             $this->addNodeAfterNode($assertSame, $node);
         }
     }
+
+    /**
+     * @param MethodCall|StaticCall $node
+     */
+    private function resolveAssertMethodName(Node $node): string
+    {
+        if (! isset($node->args[2])) {
+            return 'assertEquals';
+        }
+
+        $isStrict = $this->getValue($node->args[2]->value);
+
+        return $isStrict ? 'assertSame' : 'assertEquals';
+    }
 }
diff --git a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/assert_same_assert_equal.php.inc b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/assert_same_assert_equal.php.inc
new file mode 100644
index 00000000000..67198c34c71
--- /dev/null
+++ b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/assert_same_assert_equal.php.inc
@@ -0,0 +1,45 @@
+<?php
+
+namespace Rector\PHPUnit\Tests\Rector\MethodCall\ReplaceAssertArraySubsetRector\Fixture;
+
+use PHPUnit\Framework\TestCase;
+
+class AssertSameAssertEqual extends TestCase
+{
+    public function test()
+    {
+        $checkedArray = [];
+        $expectedSubset = ['cache_directory' => 'two'];
+
+        $this->assertArraySubset($expectedSubset, $checkedArray);
+
+        $this->assertArraySubset($expectedSubset, $checkedArray, true);
+
+        $this->assertArraySubset($expectedSubset, $checkedArray, false);
+    }
+}
+
+?>
+-----
+<?php
+
+namespace Rector\PHPUnit\Tests\Rector\MethodCall\ReplaceAssertArraySubsetRector\Fixture;
+
+use PHPUnit\Framework\TestCase;
+
+class AssertSameAssertEqual extends TestCase
+{
+    public function test()
+    {
+        $checkedArray = [];
+        $expectedSubset = ['cache_directory' => 'two'];
+        $this->assertArrayHasKey('cache_directory', $checkedArray);
+        $this->assertEquals('two', $checkedArray['cache_directory']);
+        $this->assertArrayHasKey('cache_directory', $checkedArray);
+        $this->assertSame('two', $checkedArray['cache_directory']);
+        $this->assertArrayHasKey('cache_directory', $checkedArray);
+        $this->assertEquals('two', $checkedArray['cache_directory']);
+    }
+}
+
+?>
diff --git a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/fixture.php.inc b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/fixture.php.inc
index 482dc453ca5..3ebe5144f33 100644
--- a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/fixture.php.inc
+++ b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/fixture.php.inc
@@ -10,7 +10,7 @@ class SomeTest extends \PHPUnit\Framework\TestCase
 
         $this->assertArraySubset([
            'cache_directory' => 'new_value',
-        ], $checkedArray);
+        ], $checkedArray, true);
     }
 }
 
diff --git a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2069.php.inc b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2069.php.inc
index dbc478742d9..abc8324e031 100644
--- a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2069.php.inc
+++ b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2069.php.inc
@@ -31,8 +31,8 @@ class Issue2069 extends \PHPUnit\Framework\TestCase
         $result = ['Hello' => 'a', 'World!' => 'b'];
         $this->assertArrayHasKey('World!', $result);
         $this->assertArrayHasKey('Hello', $result);
-        $this->assertSame('b', $result['World!']);
-        $this->assertSame('a', $result['Hello']);
+        $this->assertEquals('b', $result['World!']);
+        $this->assertEquals('a', $result['Hello']);
     }
 
     public function shouldWorkToo()
diff --git a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2237.php.inc b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2237.php.inc
index 7d0bd86cf68..94c7ac79b01 100644
--- a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2237.php.inc
+++ b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2237.php.inc
@@ -21,7 +21,7 @@ class Issue2237 extends \PHPUnit\Framework\TestCase
             'c' => [
                 'd' => 'item d',
             ],
-        ], $result);
+        ], $result, true);
     }
 }
 
diff --git a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2279.php.inc b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2279.php.inc
index 66684c4db30..017168f1467 100644
--- a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2279.php.inc
+++ b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/issue_2279.php.inc
@@ -10,7 +10,7 @@ class Issue2279 extends TestCase
     {
         $this->assertArraySubset([
             static::KEY_RESPONSE_BAD_REQUEST => static::VALUE_RESPONSE_BAD_REQUEST,
-        ], $parameters->getPost()->getResponses());
+        ], $parameters->getPost()->getResponses(), true);
     }
 }
 
diff --git a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/multilevel_array.php.inc b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/multilevel_array.php.inc
index 8884a53b7e6..6361745a2a4 100644
--- a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/multilevel_array.php.inc
+++ b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/multilevel_array.php.inc
@@ -15,7 +15,7 @@ class MultiLevelArray extends \PHPUnit\Framework\TestCase
             ],
         ];
 
-        $this->assertArraySubset($expectedSubset, $checkedArray);
+        $this->assertArraySubset($expectedSubset, $checkedArray, true);
     }
 
     public function otherTest()
@@ -30,7 +30,7 @@ class MultiLevelArray extends \PHPUnit\Framework\TestCase
                     ],
                 ],
             ],
-            $checkedArray
+            $checkedArray, true
         );
     }
 }
diff --git a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/variable.php.inc b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/variable.php.inc
index d4cf4f32440..85fcf760819 100644
--- a/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/variable.php.inc
+++ b/rules/phpunit/tests/Rector/MethodCall/ReplaceAssertArraySubsetRector/Fixture/variable.php.inc
@@ -11,7 +11,7 @@ class VariableTest extends \PHPUnit\Framework\TestCase
             'cache_directory' => 'new_value',
         ];
 
-        $this->assertArraySubset($expectedSubset, $checkedArray);
+        $this->assertArraySubset($expectedSubset, $checkedArray, true);
     }
 }