Assuming both are of excellent quality, on what basis do I decide which ones to purchase?
I don't have any experience crocheting.
While you've labelled the top image as "handled" due to your unfamiliarity, the correct term for that style of hook is "ergonomic," with all that name implies. They are much easier to hold onto due to the larger end, allowing those with problems with their hands to work with them, and allowing the average person to work longer.
EasyCrochet gives a nice bulleted list of benefits to ergonomic hooks:
- Achieves better tension & gauge
- Less achy hands
- Comfortable grip
- Can crochet longer without breaks
- Easier to crochet with arthritis
The primary benefit of standard hooks is that they are typically far less expensive and more accessible; for moderate improvements, you can also purchase a set of pads similar to foam pencil grips to add to them, but smaller hooks will remain very small even with this additional grip added to them. In my personal opinion, standard hooks are only of benefit to a new learner who isn't sure if they want to proceed, or someone who crochets only small projects infrequently.
Because of their very low price point and wide availability, a single basic hook and skein of yarn are a terrific starting point for the new learner; this initial learning process will also give you a better sense of what type of handle you might want to look for in moving to a more comfortable ergonomic hook, as many more styles beyond that pictured exist. I would not particularly recommend doing larger projects or working long-term with basic hooks, however, as they simply aren't all that comfortable or pleasant to work with compared to a well-suited ergonomic set.