Vacuum collapse -- why do strong metals implode but glass doesn't?

For a cylindrical pressure vessel loaded in compression (that is, vacuum inside), failure occurs by buckling instability in which a random and small inward perturbation of the stressed wall grows without bound at and beyond a certain critical load value. This is analogous to buckling instability in a thin column loaded in compression.

The characteristic which resists buckling instability is not the yield strength but the stiffness of the wall, which depends on its thickness and on its elastic modulus. The thicker the wall and the higher the modulus, the more resistant to buckling the cylinder will be.

The elastic modulus of common glass is about $48 \times 10^6$ psi compared to that of steel at $29 \times 10^6$ psi. The glass cylinder will hence be more resistant to implosion than a steel cylinder of identical size and wall thickness.

Note also that putting a scratch or microcrack in glass renders it weak in tension. In compression, however, the applied stress tends to press microcracks shut, so scratching a glass vacuum vessel does not cause the sort of catastrophic failure you expect to get when the glass is in tension.

Niels's answer is right at pointing the difference of stiffness as the main reason for the different behaviour of glass and steel. However, there is an additional element at play: relative wall thickness. In the videos, glass containers are a lot smaller than steel ones, but their walls are very thick when compared with their size - if we scaled the tubes in the last video to truck size, we would get a some inches thick wall instead of just a few mm, like the steel container.

Glass is a lot more brittle than metals under tension (as Niels said), a lot cheaper (by mass) and usually lighter. That combine to make usual glass containers a lot ticker than metal containers made for the same purpose. That's the reason we can easily crush an empty beer can with bare hands but crushing an empty beer bottle is a lot harder. The same difference holds if we replace bare hands with external air pressure.

There are two failure modes that need to be considered for a vacuum tube/vessel:

The first is tensile/compressive failure, caused by the applied stress exceeding the material's ultimate tensile stress. This is largely governed by the wall thickness and ultimate tensile stress. However, note that in a ductile material, this is preceeded by a period of plastic deformation.

The second is buckling (also known as elastic instability failure). In this case, the structure of the vessel becomes unstable to small perturbations, which can cause a failure below the load of the first case. This case is largely governed by wall thickness and elastic modulus.

Vacuum vessels made from either metal or glass can fail by either of the two modes, depending on their design and the relative values of the parameters mentioned.

Another thing to bear in mind though is that most metals are much more ductile than glass, which is very brittle. So, a failure in the two cases will look very different. A metal tube will tend to deform quite a lot before it ruptures and may 'crumple up'. However, glass cannot deform much before it breaks, so if it fails it will tend to shatter very suddenly. This tends to be more dangerous and is probably why many glass vessels have thicker walls than metal ones - because they need a higher factor of safety.