This.
We need to focus on two things in this discussion. First, the difference between accuracy and precision. Depending on the exact model of each type of instrument, it's likely that refractometers are slightly more precise than hydrometers. However, it's also probably the case that most hobby grade hydrometers are still more than precise enough for our hobby.
Think of accuracy as how close a measurement is to the real value, and precision as the resolution of the measurement. Most quality hobby grade instruments of either type are precise to three decimal places, which is arguably plenty for our hobby. So, precision isn't an issue. I like that target diagram, but it's a bit misleading in terms of portraying precision. Instead of showing a larger scatter, it should show the target zoomed out so far that you can't tell how large the scatter is. Precision doesn't imply a large scatter, it just implies a lack of resolution fine enough to know what the scatter is.
That brings up the second point. Accuracy, and the role of calibration. If you think of accuracy only as immediate repeatability, you're missing out on the role of calibration. Calibration allows you to adjust for consistently incorrect accuracy. If an instrument has a big variation in the measurements (or a lack of resolution) then calibration won't help. If an instrument is consistently wrong within the realm of its precision, you need to calibrate it.
Understanding calibration brings up another point. Understanding overall use and care of an instrument. A highly precise instrument is useless if it isn't calibrated and if it isn't used correctly. Most use and calibration mistakes introduce consistent bias (the number is always skewed in the same direction) which is a very bad thing since it introduces a false sense of confidence. You get good repeatability and a precise output, so you feel good about the reading.
How does this apply to measuring seawater? Hobby grade refractometers have use procedures that are often ignored (the common ATC units require you to leave the sample on the prism for 45 seconds before 5ak8ng a reading. How many of you do that?) They're often not calibrated consistently, and they're highly prone to drift over time. Somehow, they've earned a reputation as "better" and I wonder if this is because of the perception of precision and/or just because they're fancier and more expensive.
Hydrometers, on the other hand, are usually very consistent over time. It's telling that even fancy expensive hydrometers can't be calibrated - because they just don't drift over time. Yes, some hobby grade units come wrong out of the box, but they will pretty be consistently wrong forever, which IMHO is preferable to an instrument that drifts and is never correctly calibrated.
If you're not going to use a refractoneter correctly and calibrate it every single time you use it, you shouldn't own one.
Pick the style of instrument you like the most. Both are perfectly acceptable. Just be sure you understand how to use and calibrate it, and if in doubt (as with the OP above) test against calibration fluid from another source or against another instrument that is known good and calibrated.