Amount Completed - Finished (all puzzle pieces collected - through epilogue)
Story - Braid comes off as a standard run and jump side scroller with no story whatsoever beyond get to the end of the level / world / game. Books throughout the game reveal weird components of the story hinting towards something being masked behind a very simple presentation.
Braid apparently has an obfuscated story that does not even come close to presenting itself to me. I am clearly too naive and oblivious to pick up on the depth. In the end I just did not care to dive into the story of the game and the concepts behind it. I was simply not enticed by the story due to the overwhelmingly unique (at times) gameplay. Skimming FAQs about the game further solidified my desire to just let my knowledge of the story remain limited. The game just felt like the wrong vehicle for delivering the apparent story behind the game. I dare say the game now feels pretentious from reading about it.
Art - The style of Braid is certainly vibrant and interesting. I found the graphics effective and clear. The painted style is unique and the game art is simplistic and enjoyable. The game elements are clearly defined by their art and there is little confusion between the back and foregrounds. For a basic 2D game the art and animation is perfectly acceptable if not very good.
Gameplay - Braid at the base is a side scroller with rewind/fast-foward capability. As the player progresses through a number of world other elements are added to tweak the experience. I found that personally the difficulty of the tweaks was out of order. In one world you have a shadow that acts out your actions when you rewind time. Another world offered a ring that you could drop to slow down time within the proximity of the location you left it at. Unfortunately the previous two were after the tweak I found the most difficult. In the world before those you have to play the game where time automatically rolls forward as you move right and backward as you move left. While I struggled through the section I found that the others were more fun and a lot less frustrating/difficult.
At times I would simply make up some random goal and just haphazardly go for it. Often this would work out making me wonder if the designer intended for methodical thinking and planning or just "hoping something works out" style gameplay.
The game also is quite short if you have an idea of how to complete the puzzles... even without it will not take long to complete.
Gut - Fun at times, frustrating at other times. If you are looking for a story, look elsewhere unless you really like to unravel and explore layers of references and otherwise in your side scrollers.