A one-piece curb cap is preferable. it allows a tighter seam to prevent leaks.

Hi Bellycat! When I saw your question I was surprised at how much I had to say about such a seemingly simple thing. So, here goes!! My greatest concern in a shower, or wet environment, is ease of cleaning and keeping it clean. Anywhere there is grout, the surface is rough and slightly recessed. That means it stays wet longer and the rough surface gives mildew a place to hide. The less grout the better, in my opinion! However, using something like a travertine or marble slab usually means there will be a slight overhang either on one side or both. The overhang results in a space under it that is hard to get at to clean, again, mildew. Also, natural stone products are very susceptible to pitting from cleaning products. Even vinegar will damage them. Once you have a pitted surface, you might as well have grout. See the problem?? LOL! I think if the shower curb is constructed using the proper materials, leaking shouldn't be a problem. The curb doesn't typically get, or stay, nearly as wet as the shower floor, and shower floors are tiled and grouted all the time. I guess when weighing the pros and cons of each, I would vote for tile. It is what I used in my own shower.

@Design Distinctions - nothing simple about this question :) Just wish I had known before picking out tile as no easy match. Leaning toward an ivory travertine or almond on white or almond on almond marble for cap and sink; just hope it looks good with the tiles I so painstakingly picked out. UGH!