Yes, I feel like Square Enix tries to make its sequels stand out from their predecessors with only a few exceptions. My personal tastes for a sequel revolve around the close correlation between a sequel and its predecessor. Like I said before, one of my favorite pairs of games is Lunar: The Silver Star and Lunar: Eternal Blue because both games keep a consistent feel and gameplay mechanics.
If we look at some of the more recent Square Enix sequels like Final Fantasy VII and Final Fantasy VII Dirge of Cerberus, then we see a striking difference that turns fans of the original game away. If we look at specific instances like Final Fantasy IV and Final Fantasy IV: The After Years, then we see most people pleased with the gameplay at the very least as it is essentially the same game at its core.
My recommendation to game developers is that they try not to stray too far with the original material and appeal to the fans of the original game. For example, I wonder if a sequel in the Compilation of Final Fantasy VII would have been better received if it took was very similar to Final Fantasy VII in gameplay? What if the story was about a new cast of characters, with some returning characters like Marlene and Denzel, in a world Twenty Minutes Into The Future? No, you might not be happy with the story, but you would at least be happy with the returning gameplay and updated graphics of a game that you loved at the very least.
Final Fantasy XIII has its share of fans, too. I hope it sticks closely to the original with some minor changes to address player complaints rather than try to reinvent the wheel while only recycling existing graphics and story elements.