I was an Ultimate player before I ever played disc golf, so the feel of slight grooves for the thumb was natural. My son (also an Ultimate Frisbee Player) got an Ultra Luna as part of a Battle pack and loves it. It is his Go to approach disc. 

When it came out in the base plastic I thought I'd give it a shot. It's got a nice true stable flight. You can manipulate it to any angle you want, but it does fade out a little bit, just a little putter fade. The Luna is of course a great feeling and flying putter, used by one of the greatest disc golfers of all time, and so the Ultra Luna is also a great disc, just with a little different feel on the thumb. I really like it. It's a good throwing putter for me.

Do the grooves offer any noticeable advantage for me? 

No. But they don't bother me either and it kind of gives me more confidence. So if you like something just a little bit different or are an Ultimate player familiar with grooves on an Ultra-Star, you're probably going to really like the Ultra-Luna. Solid disc, but not something I am going to permanently bag.