diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 6c44b7759f0e29..46f2cbb2ebeefc 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -704,7 +704,13 @@ def _cmp_method(self, other, op):
         if isinstance(
             other, (ArrowExtensionArray, np.ndarray, list, BaseMaskedArray)
         ) or isinstance(getattr(other, "dtype", None), CategoricalDtype):
-            result = pc_func(self._pa_array, self._box_pa(other))
+            try:
+                result = pc_func(self._pa_array, self._box_pa(other))
+            except pa.ArrowNotImplementedError:
+                # TODO: could this be wrong if other is object dtype?
+                #  in which case we need to operate pointwise?
+                result = ops.invalid_comparison(self, other, op)
+                result = pa.array(result, type=pa.bool_())
         elif is_scalar(other):
             try:
                 result = pc_func(self._pa_array, self._box_pa(other))
diff --git a/pandas/core/arrays/string_arrow.py b/pandas/core/arrays/string_arrow.py
index 7119f6321a7ffb..00d92958cc8dc4 100644
--- a/pandas/core/arrays/string_arrow.py
+++ b/pandas/core/arrays/string_arrow.py
@@ -37,7 +37,6 @@
     BaseStringArray,
     StringDtype,
 )
-from pandas.core.ops import invalid_comparison
 from pandas.core.strings.object_array import ObjectStringArrayMixin
 
 if not pa_version_under10p1:
@@ -565,10 +564,7 @@ def _convert_int_dtype(self, result):
         return result
 
     def _cmp_method(self, other, op):
-        try:
-            result = super()._cmp_method(other, op)
-        except pa.ArrowNotImplementedError:
-            return invalid_comparison(self, other, op)
+        result = super()._cmp_method(other, op)
         if op == operator.ne:
             return result.to_numpy(np.bool_, na_value=True)
         else:
diff --git a/pandas/tests/series/test_logical_ops.py b/pandas/tests/series/test_logical_ops.py
index d3a718be47c18d..ff21427b71cf9e 100644
--- a/pandas/tests/series/test_logical_ops.py
+++ b/pandas/tests/series/test_logical_ops.py
@@ -9,6 +9,7 @@
 from pandas.compat import HAS_PYARROW
 
 from pandas import (
+    ArrowDtype,
     DataFrame,
     Index,
     Series,
@@ -539,18 +540,38 @@ def test_int_dtype_different_index_not_bool(self):
         result = ser1 ^ ser2
         tm.assert_series_equal(result, expected)
 
+    # TODO: this belongs in comparison tests
     def test_pyarrow_numpy_string_invalid(self):
         # GH#56008
-        pytest.importorskip("pyarrow")
+        pa = pytest.importorskip("pyarrow")
         ser = Series([False, True])
         ser2 = Series(["a", "b"], dtype="string[pyarrow_numpy]")
         result = ser == ser2
-        expected = Series(False, index=ser.index)
-        tm.assert_series_equal(result, expected)
+        expected_eq = Series(False, index=ser.index)
+        tm.assert_series_equal(result, expected_eq)
 
         result = ser != ser2
-        expected = Series(True, index=ser.index)
-        tm.assert_series_equal(result, expected)
+        expected_ne = Series(True, index=ser.index)
+        tm.assert_series_equal(result, expected_ne)
 
         with pytest.raises(TypeError, match="Invalid comparison"):
             ser > ser2
+
+        # GH#59505
+        ser3 = ser2.astype("string[pyarrow]")
+        result3_eq = ser3 == ser
+        tm.assert_series_equal(result3_eq, expected_eq.astype("bool[pyarrow]"))
+        result3_ne = ser3 != ser
+        tm.assert_series_equal(result3_ne, expected_ne.astype("bool[pyarrow]"))
+
+        with pytest.raises(TypeError, match="Invalid comparison"):
+            ser > ser3
+
+        ser4 = ser2.astype(ArrowDtype(pa.string()))
+        result4_eq = ser4 == ser
+        tm.assert_series_equal(result4_eq, expected_eq.astype("bool[pyarrow]"))
+        result4_ne = ser4 != ser
+        tm.assert_series_equal(result4_ne, expected_ne.astype("bool[pyarrow]"))
+
+        with pytest.raises(TypeError, match="Invalid comparison"):
+            ser > ser4