diff --git a/swh/storage/db.py b/swh/storage/db.py
--- a/swh/storage/db.py
+++ b/swh/storage/db.py
@@ -1121,9 +1121,7 @@
             ({', '.join(_object_metadata_insert_cols)})
         VALUES ({', '.join('%s' for _ in _object_metadata_insert_cols)})
         ON CONFLICT (id, authority_id, discovery_date, fetcher_id)
-        DO UPDATE SET
-            format=EXCLUDED.format,
-            metadata=EXCLUDED.metadata
+        DO NOTHING
     """
 
     object_metadata_get_cols = [
diff --git a/swh/storage/tests/test_storage.py b/swh/storage/tests/test_storage.py
--- a/swh/storage/tests/test_storage.py
+++ b/swh/storage/tests/test_storage.py
@@ -3227,8 +3227,13 @@
 
         result = swh_storage.content_metadata_get(content_swhid, authority)
         assert result["next_page_token"] is None
-        assert [data.content_metadata, new_content_metadata2] == list(
-            sorted(result["results"], key=lambda x: x["discovery_date"],)
+
+        expected_results1 = (data.content_metadata, new_content_metadata2)
+        expected_results2 = (data.content_metadata, data.content_metadata2)
+
+        assert tuple(sorted(result["results"], key=lambda x: x["discovery_date"],)) in (
+            expected_results1,  # cassandra
+            expected_results2,  # postgresql
         )
 
     def test_content_metadata_add_dict(self, swh_storage):
@@ -3473,8 +3478,14 @@
 
         result = swh_storage.origin_metadata_get(origin["url"], authority)
         assert result["next_page_token"] is None
-        assert [data.origin_metadata, new_origin_metadata2] == list(
-            sorted(result["results"], key=lambda x: x["discovery_date"],)
+
+        # which of the two behavior happens is backend-specific.
+        expected_results1 = (data.origin_metadata, new_origin_metadata2)
+        expected_results2 = (data.origin_metadata, data.origin_metadata2)
+
+        assert tuple(sorted(result["results"], key=lambda x: x["discovery_date"],)) in (
+            expected_results1,  # cassandra
+            expected_results2,  # postgresql
         )
 
     def test_origin_metadata_add_dict(self, swh_storage):