Almost universally people seem to suggest/imply that "better" tools are important and worth the price difference.
That certainly used to be a worthwhile general shopping guide, one that is repeated in many early woodworking books that I've read (the same principle is repeated outside of woodworking circles too of course).
But to be honest I'm not sure it has ever been universally true. And it's absolutely not the case today that high price guarantees quality, or that low price automatically means you're buying a mediocre or outright poor tool.
Many of the bigger name brands are not the same company that they were, and their name (and the consequent higher/high price commanded by their tools) are not in any way an assurance of high quality. Perhaps the best example of this in the broader woodworking scene is Stanley; the current company has for all intents and purposes zero relationship to the Stanley of old, except that they own the name. Even by the latter part of the 20th century Stanley's standards had slipped noticeably, and now much of their product line is considered from mediocre to outright junk, depending on whose opinion you're listening to.
A great illustration of the potential for high quality at a low price (note: low, not lower) are the bevel-edge chisels sold by Aldi. Their reputation has spread online due in no small part to Paul Sellers in the UK plugging them so consistently. And he's right to, as I think they still are the cheapest chisels on the UK market while still being full size, and featuring hardwood handles and not moulded plastic. Their qualities, as judged by many experienced woodworkers including Sellers, are right up there with some competitors that cost upwards of five times more.
Some people have gone so far as to say "whatever you do don't get the ones made in China." Why not?
That's a very good question and cuts right to the heart of tool prejudices (and dare I say it, may even be a form of racism).
The simple fact of the matter is that this is an opinion and you can be assured that anyone who says that everything made in China is junk, or should be avoided on principle, is ill-informed and outright wrong. The Aldi chisels mentioned just above? They are of course made in China.
What's particularly sad about this is many of the tools that these same people buy, from some name brands they trust, are now also made in China. Which highlights how foolish it is to make that kind of sweeping condemnation.
They both seem to be made of high speed steel (which I'm told is important and what I want).
It is important but it's not necessarily what you want. HSS could almost be considered obsolete for turning tools (almost) because carbide-tipped tools are now on the market, offering far longer service life — reducing the constant need to re-sharpen that has dogged turners since, well, forever.
The sharpening of turning tools shouldn't be downplayed: in turning you may sometimes have to sharpen multiple times before the shaping of a single project is completed. So a grinder should be factored in as not just a desirable additional purchase, but almost a necessity.
Is one more durable?
It's possible, but I wouldn't want to say in which direction TBH.
Note that the "HSS" label is just a starting point, it doesn't really guarantee anything specific. In addition to HSS being an inherently tough steel type with good hardening properties, the exact alloy used (there are a few), and the way the tool was formed in the factory are critical factors.
It's much the same as with basic high-carbon tool steel, as used pretty universally 100 years ago for all sorts of cutting tools; it didn't mean that all chisels or plane irons produced at the time were of equal quality.
Is handle shape/material of any importance?
Yes and yes, but personal preferences are very important here.
Many turners make it a point to turn their own tool handles to suit their individual tastes on the ideal handle shape (often going for a much long handle for example), and will go so far as to immediately replace the handles on expensive chisels they just bought.
Re. material, once you pass a certain strength the type of hardwood doesn't appear to matter that much. It would seem from practical experience that material properties like vibration dampening (a traditional reason that ash was favoured) aren't as critical as was/is supposed, given than many people are very happy with handles made from maple, rosewood, even ebony, none of which share this characteristic. These days plastics and even the occasional metal handle are seen, which again argues strongly that material qualities are not a critical factor except in terms of what the user likes or doesn't like.