Weave/Star
To me, it seems like the success with either one of these patterns doesn't lie within the pattern itself...but rather...like many aspects of DK...success lies within the leniency of the randomness.
Sure, you can make an educated guess and decide whether or not to do the star/weave based on how firefoxes are dispersed throughout the screen...as you clear the first rivet...but any firefox can spoil either pattern if you get unlucky. It only takes 1 stubborn firefox running left to block you from either climbing up to clear the top left rivets (star/weave), climb down to grab the left hammer (star), or prevent you from getting the middle hammer (star/weave).
You're at the mercy of the game...and I don't think either pattern is superior over the other...nor do I think one can accurately judge whether or not to use either pattern based on what happens during the first 5-6 seconds of the screen.
You never hear anyone shouting "do the weave, weave!" or, "go for the star, star!"...you always hear people say, "maybe the weave would have worked there", or, "probably shoulda just stuck with the star"...and thats just hindsight.
Just my 2 cents.