The sediment forming the edge of the second hole appears to be more like lake mud and silt than the ash and lapilli in the first, older, hole. However, I didn't look all that carefully at the stratigraphy here- the same mud and silt (which appears to be more easily eroded) may have been removed over the years since the original hole opened up. In other words, given a few years of erosion, this hole may come to look the same as the old one.
Also, as you can see, this hole is still draining the lake in early September. We had our first significant rain of the season yesterday and this morning, and I'd bet the pass area got much more rain than we did down here in the valley. While the next week is forecast to be dry and very pleasant, it won't be too long before both holes are submerged again.