Why did ancient Qin-Han era crossbow bolts have a tang but medieval European crossbow bolts seem to lack tangs? From the pictures I've seen, the ancient Qin-Han era bolts have a metal head and a metal tang that is inserted into a wooden shaft. The metals used is bronze, iron/steel, or a combination of both (ie. tip/head and tang can be different metals). The medieval European crossbow bolts on the other hand, seem to all be of a socket construction where the arrow head directly wraps around the socket.
Is anyone familiar with the pros and cons of each type?
Images for comparison: https://imgur.com/a/jZfhCGN
Edit: Apparently Wootan_weevil pointed out that there are medieval European crossbow bolts with tangs too...so my original assumption is sort of invalidated. It seems that Eastern Eurasia and Western Eurasia used both tanged and socketed construction, with some favoring the other depending on the time frame. https://www.metmuseum.org/art/collection/search/33644
It's easier to make tanged forged arrowheads or bolt heads than socketed forged arrowheads or bolt heads. To forge a socket, you need to first make a flat section and then wrap it around a mandrel. Thus, the earliest metal arrowheads, which were forged copper or bronze, were tanged. Socketed bronze arrowheads are cast (and often have complex heads such as heads with midribs or triblobate heads, shapes which are difficult to forge, but increase the stiffness of the head).
A tanged arrowhead can also (a) be lighter than a socketed arrowhead with a blade of the same size, or, if the tang is much longer than the socket, can (b) strengthen the foreshaft of the arrow.
The disadvantage of tangs is that it is harder to fit the head to a wooden arrow shaft. This can be done by splitting the shaft, inserting the tang, and gluing and/or binding the end of the shaft, or by burning the tang in (possibly after drilling a pilot hole). To fit a socketed head, just taper the end of the shaft, and glue the head on. There are two further advantages/disadvantages:
A tanged head can be attached more securely, and is less likely to come off the arrow when the arrow is extracted from the target (which can be either an advantage or disadvantage).
A tanged head can result in the shaft splitting on impact.
If using hollow bamboo or cane for the shaft, a tanged head can be easier to attach, but the end of the shaft should still be bound.
As you note, tanged heads were usual in East Asia, at least for military arrows and crossbow bolts. Tanged heads were also common in early Medieval Europe, with socketed heads becoming common in the later Medieval period. Some tanged heads were still in use in this period, but were a minority. One of the images in your imgur album shows a tanged head alongside 3 socketed heads:
and these crossbow bolts include 2 tanged heads and 3 socketed heads:
Socketed heads were not unknown in East Asia, but were usually used on target arrows (i.e., practice arrows) rather than war arrows:
These target heads are essentially just a socket, a hollow cap that fits over the end of the shaft (some modern field points AKA target points are made like this, too).