The actual values of the custom fields are stored in the WordPress table wp_postmeta and of course would be in the Exported file. But, in addition to the values of the field, Magic Fields also needs to know the field and group index of the field. (Magic Fields support repeated fields and repeated groups.) These indexes are stored in the proprietary table wp_mf_post_meta.
mysql> show columns from wp_mf_post_meta;
+-------------+--------------+------+-----+---------+-------+
| Field | Type | Null | Key | Default | Extra |
+-------------+--------------+------+-----+---------+-------+
| meta_id | int(11) | NO | PRI | NULL | |
| field_name | varchar(255) | NO | | NULL | |
| field_count | int(11) | NO | | NULL | |
| group_count | int(11) | NO | | NULL | |
| post_id | int(11) | NO | MUL | NULL | |
+-------------+--------------+------+-----+---------+-------+
5 rows in set (0.07 sec)
The columns field_count and group_count are the field index and group index of the custom field with the given meta_id. This information is necessary as a given field name can have multiple rows in wp_postmeta if the field or group is repeated. And even if you did not repeat the group or field the index information is required. Otherwise when you use get( $field_name, $group_index=1, $field_index=1, $post_id=NULL ) to access the field it would fail to find the indexes (in this case [1,1]) in wp_mf_post_meta. Are the index data also in the Exported file?
Types only use the standard WordPress tables but its feature set is different from Magic Fields 2. In particular, Magic Fields 2 has a very useful related_type field that Types does not have an equivalent for – that was a deal breaker for me.