diff --git a/skbase/utils/deep_equals/_deep_equals.py b/skbase/utils/deep_equals/_deep_equals.py
index 425408ec..32c3bc51 100644
--- a/skbase/utils/deep_equals/_deep_equals.py
+++ b/skbase/utils/deep_equals/_deep_equals.py
@@ -150,6 +150,7 @@ def _pandas_equals_plugin(x, y, return_msg=False, deep_equals=None):
 
 
 def _pandas_equals(x, y, return_msg=False, deep_equals=None):
+    import numpy as np  # pandas depends on numpy, so this import is fine
     import pandas as pd
 
     ret = _make_ret(return_msg)
@@ -173,13 +174,68 @@ def _pandas_equals(x, y, return_msg=False, deep_equals=None):
         else:
             return ret(x.equals(y), ".series_equals, x = {} != y = {}", [x, y])
     elif isinstance(x, pd.DataFrame):
+        # check column names for equality
         if not x.columns.equals(y.columns):
             return ret(
-                False,
-                ".columns, x.columns = {} != y.columns = {}",
-                [x.columns, y.columns],
+                False, f".columns, x.columns = {x.columns} != y.columns = {y.columns}"
             )
         # if columns are equal and at least one is object, recurse over Series
+        # check dtypes for equality
+        if not x.dtypes.equals(y.dtypes):
+            return ret(
+                False, f".dtypes, x.dtypes = {x.dtypes} != y.dtypes = {y.dtypes}"
+            )
+        # check index for equality
+        # we are not recursing due to ambiguity in integer index types
+        # which may differ from pandas version to pandas version
+        # and would upset the type check, e.g., RangeIndex(2) vs Index([0, 1])
+        xix = x.index
+        yix = y.index
+        if hasattr(xix, "dtype") and hasattr(xix, "dtype"):
+            if not xix.dtype == yix.dtype:
+                return ret(
+                    False,
+                    ".index.dtype, x.index.dtype = {} != y.index.dtype = {}",
+                    [xix.dtype, yix.dtype],
+                )
+        if hasattr(xix, "dtypes") and hasattr(yix, "dtypes"):
+            if not x.dtypes.equals(y.dtypes):
+                return ret(
+                    False,
+                    ".index.dtypes, x.dtypes = {} != y.index.dtypes = {}",
+                    [xix.dtypes, yix.dtypes],
+                )
+        ix_eq = xix.equals(yix)
+        if not ix_eq:
+            if not len(xix) == len(yix):
+                return ret(
+                    False,
+                    ".index.len, x.index.len = {} != y.index.len = {}",
+                    [len(xix), len(yix)],
+                )
+            if hasattr(xix, "name") and hasattr(yix, "name"):
+                if not xix.name == yix.name:
+                    return ret(
+                        False,
+                        ".index.name, x.index.name = {} != y.index.name = {}",
+                        [xix.name, yix.name],
+                    )
+            if hasattr(xix, "names") and hasattr(yix, "names"):
+                if not len(xix.names) == len(yix.names):
+                    return ret(
+                        False,
+                        ".index.names, x.index.names = {} != y.index.name = {}",
+                        [xix.names, yix.names],
+                    )
+                if not np.all(xix.names == yix.names):
+                    return ret(
+                        False,
+                        ".index.names, x.index.names = {} != y.index.name = {}",
+                        [xix.names, yix.names],
+                    )
+            elts_eq = np.all(xix == yix)
+            return ret(elts_eq, ".index.equals, x = {} != y = {}", [xix, yix])
+        # if columns, dtypes are equal and at least one is object, recurse over Series
         if sum(x.dtypes == "object") > 0:
             for c in x.columns:
                 is_equal, msg = deep_equals(x[c], y[c], return_msg=True)
@@ -189,7 +245,14 @@ def _pandas_equals(x, y, return_msg=False, deep_equals=None):
         else:
             return ret(x.equals(y), ".df_equals, x = {} != y = {}", [x, y])
     elif isinstance(x, pd.Index):
-        return ret(x.equals(y), ".index_equals, x = {} != y = {}", [x, y])
+        if hasattr(x, "dtype") and hasattr(y, "dtype"):
+            if not x.dtype == y.dtype:
+                return ret(False, f".dtype, x.dtype = {x.dtype} != y.dtype = {y.dtype}")
+        if hasattr(x, "dtypes") and hasattr(y, "dtypes"):
+            if not x.dtypes.equals(y.dtypes):
+                return ret(
+                    False, f".dtypes, x.dtypes = {x.dtypes} != y.dtypes = {y.dtypes}"
+                )
     else:
         raise RuntimeError(
             f"Unexpected type of pandas object in _pandas_equals: type(x)={type(x)},"
diff --git a/skbase/utils/tests/test_deep_equals.py b/skbase/utils/tests/test_deep_equals.py
index 271cf135..d8a3b219 100644
--- a/skbase/utils/tests/test_deep_equals.py
+++ b/skbase/utils/tests/test_deep_equals.py
@@ -36,6 +36,7 @@
     EXAMPLES += [
         pd.DataFrame({"a": [4, 2]}),
         pd.DataFrame({"a": [4, 3]}),
+        pd.DataFrame({"a": ["4", "3"]}),
         (np.array([1, 2, 4]), [pd.DataFrame({"a": [4, 2]})]),
         {"foo": [42], "bar": pd.Series([1, 2])},
         {"bar": [42], "foo": pd.Series([1, 2])},