I like it, it's a brave choice for a Batman movie costume, literally every other incarnation of the cinematic suit has been one thing: black rubber armor with tall ears. From what I can tell we've got a very comic book faithful costume, gray on black colors, and the short ears featured heavily in Batman's origins, 60s show, Frank Millers work, etc etc. The short ears are as much Batman as the longer ears are.
Very excited about seeing more of this suit and the Batmobile, I think they both look fantastic in these teasers.
About the tail fin from the previous movies looking cheap and wobbly, I suspect that's because they were cheap and wobbly. The Batmobile from Batman and Robin was extremely over the top, anytime it moved everything shook. The tail fin on this one appears to be machined metal, I doubt it will wobble like the cheap plastic fins on the B&R batmobile.