The technological advancements over centuries are often hard to grasp. Sometimes I like to wonder if a basic tool, such as a kitchen knife would be a good benchmark for it.
If we consider an OK everyday knife, e.g. Ikea https://www.ikea.com/us/en/p/ikea-365-3-piece-knife-set-90341170/ worth ~$20, would it roughly compare to an european medieval knife in terms of quality and durability? (except for stainless steel material). How large portion of household's wealth would it be?
I'm going to mostly center this around medieval London.
Assuming we took our time machine and warped an Ikea knife back 1000 years or so, from at least a technical standpoint, yes, it'd be better.
It wasn't economical to use steel for the entirety of a medieval knife as it needed to be imported. (Generally less steel than, say, swords.) Knives were typically forged out of wrought iron, and in order to get the sharp edge, a harder steel portion was added. There could be variety in this; for example, it was possible to even have simply just wrought iron strips welded together, or an iron core with a steel edge wrapped around.
(In a survey of knives in medieval Russia, with more plentiful access to steel appropriate for such a use, there were knives made of layers of steel and iron. It still wasn't common to have an all-steel construction, though.)
This means, quite definitely, the modern knife is stronger, even putting aside the fact that modern manufacturing processes and metallurgic knowledge allow for higher consistency.
This isn't the entirety of the situation, though. Technology is also affected by culture. And the important question upon a medieval mind seeing the Ikea knife is what they'd categorize it as.
There were essentially two knife constructions in use, the "whittle tang" and the "scale tang". The whittle tang has the main part go back into the handle (sort of a hidden spike in the handle) whereas the scale tang has material (the handles or "scales") riveted to the top. (This terminology is also used for modern knives.)
The whittle tang was considered more of a general purpose blade, and it was of the type an average medieval person would have in a scabbard that is carried everywhere they go. For eating, it was both their tool for cutting food as well as their utensil, and they often had decorative elements as they were something of a personal statement. (You would not share your knife with others.) This cultural tendency lasted quite a long time and you can even see in this 1640 painting by H. H. Kluber women with red dresses and knives attached to their waists. The Ikea knife would not be sutable for such a use (and even without the excessive size, the decorative aspect to the end might be considered inferior).
The scale tang design generally would be categorized by the medieval mind as a cleaver. Modern cleavers tend to have entirely flat cutting edges, but for the medieval butcher they would use the back flatter part of their blade for that purpose because they would also need the front part for a wider variety of cuts. Cleavers would be able to cut bone, knives would be for anything softer.
While I'm just again basing all this on a picture, while the Ikea knife might work for small animals, it wouldn't work too well for higher bone density. A butcher would also want the knife to be heavier as rather than applying force which would potentially break the knives they're used to (remember, the majority of their knife body would be iron) they would be relying on the weight of the knife to do the cut.
So, in summary: what would actually happen, assuming our time-warped knife dropped into medieval London. 1. people would assume it was for butchery because of the scale tang design 2. a butcher would try to use it but find it not thick enough to cut bone. In other words, your standard kitchen knife would not meet the cultural function of knives at the time so wouldn't be as useful as you'd think. Our theoretical medieval butcher may still have been able to figure out how to put the device to good use -- the archaeological record on specialty knives is scarce enough that they may even have had something similar -- but if we're talking about raw financial value, probably the fact the entire Ikea knife is steel is the most noteworthy part, and the best route might be to simply melt it down for the high-quality steel in order to fashion something else.
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Ottaway, P. (1988). J. Cowgill, M. Neergaard de & Griffiths N. Medieval Finds from excavations in London 1: Knives and scabbards. London: HMSO for the Museum of London.
Seetah, K. (2018). Humans, Animals, and the Craft of Slaughter in Archaeo-Historic Societies. United Kingdom: Cambridge University Press.
I cannot answer the question but can point you to another question answered here by /u/angry-mustache and /u/wotan_weevil who may be able to provide some answer now if this link doesn't help.