In terms of assessing a knife you have in hand, you should start cutting with it. Then ask yourself:
1) (Food release) Does food stick to the side of it? Assuming you’re right handed, the cut food will usually be sticking to the right side of the knife. Some of this is inevitable, but there’s a huge spectrum ranging from “a half-potato gets suctioned to the knife so strongly that you can’t shake it off” to “small pieces of minced garlic and onion stick, but larger product always falls off”. Knives with better food release tend to have more curvature on the right side. This can be convexity, or concavity. Obviously you’d prefer food to release more easily, but there’s a tradeoff with
2) (Food separation) How easily does the knife move through food? Carrots are beloved as test subjects, but you can also try slicing an apple in half. If your knife gets stuck in the product, that’s “wedging” and is usually considered undesirable. If you hear a lot of “cracking” when you cut, that’s also undesirable, since it indicates that the food is not being cleanly cut, but rather wedged apart. Also, just feel for the ease of the cut. Note that a lot of this (and food release, too) is dependent on technique. For instance, your knife will wedge must less if there is some horizontal movement to your knife instead of just a straight-down-through-the-product movement. Food separation is mostly a measure of how thin the knife is, especially just “behind the edge”. However, a little bit of convexity in the blade geometry can actually help with food separation too, since if the sides of your knife are very flat the blade might have more “stiction” as you push it through food. Another thing to note is that food separation may be different in different parts of the blade. Many knives have “distal taper”, meaning the knife gets thinner (eg 4mm -> 1mm) as you proceed from the handle to the tip. You can really tell if a knife has distal taper, or just a thin tip, when you do horizontal cuts in onions. With good technique and a little speed, the tips of most knives will go through onions horizontally just fine, but some require better technique and more speed than others.
3) (The profile) Is the edge too flat or too curved? Is the tip too high or too low? An edge that is too curved may result in “accordion cuts”, where if you chop straight down, the product doesn’t completely separate near the base. (This can be mitigated with good technique.) An edge that is too flat may clunk against the board when you push forward, and may also result in accordion cuts if your cutting board is not flat. A high tip will help with rock chopping, a low tip helps if you “pull cut”, ie cut with a significant horizontal component to the movement toward you, since then you don’t have to jack up your elbow as you do it. A low tip may stick into the board if you’re not careful. Profile preferences vary depending on cutting technique, and obviously the phrases “too flat / too curved” can describe different sections of the knife, not just the whole profile.
4) (The steel and heat treatment) How nice does it feel to sharpen? How sharp can you get it? How long does it stay sharp? Does it chip easily, or does the edge fold over? How reactive is it? Different steels, and different treatments of the same steel, will feel very different on whetstones (and a given steel may even feel different on different stones). If you sharpen a lot, you probably care about this feeling. Some steels make it easier to get an acute, refined apex. Some steels are naturally “toothier”, meaning you end up with more microserrations on the edge after sharpening. A lot of this is dependent on the stones and your technique, but the steel matters too. The length of time a knife will stay sharp also varies a lot with the steel and its treatment. Of course, the sharpness of a knife degrades is really a (possibly nonlinear) curve, e.g. with some steels like VG-10, the edge will very quickly degrade from “insanely sharp” to “reasonably sharp”, and then will stay like that for a long time. So the “edge retention” of a knife is not just a quality that can be assessed with a single numerical grade. Also, the way in which an edge can degrade can vary. Very hard steels often microchip, soft steels tend to fold over. Sometimes, very slight microchipping can be kind of nice, e.g. I’ve noticed that my Heiji semistainless petty seems to get more toothy as it dulls, but for the most part it’s not welcome. All this depends a lot on the exact type of edge you’re putting on your knife, though, not just on the steel. Finally, some (carbon steel) knives will react more than others when in contact with water or food. If the knife is “clad” (ie a hard core steel sandwiched between layers of softer metal), the different metals may react differently. Soft iron cladding is usually the worst of the bunch in terms of reactivity, but it’s also really easy to thin and polish. And many of us really like patina on our knives. It’s a little nonstick and looks nice.
5) (Other stuff) Does it looks nice? Is the handle well constructed, well installed and comfortable? Are the spine and choil (the vertical non-sharp edge of the blade that’s directly in front of the handle) of the knife rounded, eased, or just really sharp and unpleasant to touch? Does the kanji (the characters written on Japanese knives) look like it was written by a 5 yr old? Is the finish well done, or is it splotchy with lots of errant scratches? If the knife has a wide bevel, are there lots of high and low spots that make it difficult to polish on flat whetstones? (You may not be able to see these spots easily unless you try to polish it.) Where is the balance point of the knife? (Some prefer a forward balance, which gives greater control of the tip, and some prefer a balance more toward the handle, which makes the knife whippier and more maneuverable.) How was the edge of the knife out of the box? (This is important if you don’t sharpen, but not important at all if you do, as you should. Although sometimes it’s annoying if a knife comes with like no edge whatsoever and you have to do a lot of work setting a bevel immediately.) Is the box nice? Does it come with a handwritten note thanking you for your loyalty to Japanese Knife Imports?
or convex 
? Beyond that, weight can give you an idea. Handle type and weight. Other members opinions taken with a grain of salt. Some makers are consistent. Others all over the place.
