Both plants have brilliant red/purple foliage and light purple blooms. Sparkling Burgundy was discovered at Plant Delights Nursery in North Carolina (South Carolina?), and, I believe, was the first purple eucomis, so it's probably better known. Oakhurst was discovered in a San Diego, California nursery. I suspect there may be a slight difference in their size, with SB being a few inches taller, but I have not seen Oakhurst.

I have seen Sparkling Burgundy at the Atlanta botanical garden. It is a very dramatic plant, in bloom or out of bloom. I have not grown it, but it's on my list for "eventually". I have three varieties of eucomis and have found them to be very easy to grow here.

It would be easier to answer your questions if you will include your state and climate zone in the future. :)