You can install either one. The 60-amp subfed panel would require a 60-amp breaker in the 100-amp panel to feed it. The 100-amp sub-fed panel could be fed using feed-through lugs, no additional breaker required (lug out of the 100amp panel, main lugs only on the subfed panel).
Some jurisdictions (including Chicago) require a main breaker at all panels and/or don't permit subfeed lugs, beware of that.
Busbar's reference to 450-3 means that the max breaker for the transformer secondary is 200 amps, anything less than that is OK for the transformer.
But your panels are only rated for 100 amps, so the maximum breaker you can use is 100 amps to protect the panel bus. You can certainly use a single 100-amp breaker to protect two panels in series (unless the local AHJ has an issue as previously mentioned), they are both 100-amp panels and the breaker will limit the current they see to a maximum of 100 amps. I suppose the appropriate Code reference for that would be 240.4, which requires that conductors be protected against overcurrent.