Which is better? If there is no winner what are the differences performance wise.
H is more stable and V is more fast. W is in the middle and O is more relaxed.
I bet TA could rap to that 
My O yoyos seem to be harder to hit tricks with, meaning they take more concentration, the opposite of relaxed. 
I like a strong H-shape like the Super G or an undercut H-shape like the Cliff. I also enjoy O-shapes like the AC2, Avalanche, and Sasquatch.
V = super easy to catch
H = more stable (in theory)
O = comfortable rounded
W = easy to catch and a little more stable (in theory)
That’s how I very very broadly categorize them. Size, weight, bearing, etc. can impact so much I mostly look for what’s comfortable. For me, I love how technical I can get with a small V but for general use and comfort I gravitate toward O. MMC, Cascade, WM2 to be specific. Amplitude for fast V.
My “best” shape would probably be an undersized combination of them all - which is why I’m so excited about ODRebirth - if it even turns into a real thing.
Those aren’t O
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Less stability makes them more prone to spinning out if you’re not landing the string dead center… I agree that this is not “relaxing” 
“Relaxed” is another one of those odd characteristics (like floaty) that’s commonly used to describe some yoyos… I kinda interpret “relaxed” to mean “not particularly fast”
At my limited skill level, I feel like rounded profile yoyos, while easy to get a good solid throw (and therefore great for just starting out) are not so great once you start trying to learn more complex string tricks. My first yoyo (Chico Bulldog 225) is a round profile, and at this point I use it primarily just to validate that I’ve gotten fairly proficient with a trick… i.e. if I can get through it well, without spinning out, with the Bulldog, then the trick is solid.
Maybe round profile yoyos have some other merits that I’ve not yet come to appreciate.
What’s differentiates an H from a W? (Never really considered W as a separate shape before)
W is like a V, but there are two angles instead of one. YYF Onestar
H has straight or just slightly angled sides by a large gap, then expands out to a hub around the axle. YYF Regen
“W” is a new designation as far as I can tell, invented for the latest Benchmark series.
It used to be just called “V” also, or in some cases and by some stores “stepped straight”.
The main benefit of “O” yoyos IMO… comfort! Nomad feels lovely to catch, while Krown (even though it’s a favourite) isn’t exactly comfy. It’s very satisfying to bind a fast-spinning yoyo from any kind of bind and feel confident that it’s going to feel great when it hits the hand.
Some yoyos you just don’t want to bind and catch when they still have a hard spin going on.
The weight distribution TENDS to also be more “neutral”. I don’t know why, but people seem to like extremes. With the apparent dominance of rim-weighted yoyos for so long (and V or H shapes to emphasize that rim weight) sometimes it’s nice to play something a bit livelier. More resistant to tilt (ie. “stable”) is seen as desireable but it costs the ability for fast correction and are less responsive during plane-shifting tricks.
Diff’rent strokes… I will always have a place for O-shaped yoyos in my collection.