Ungrounded is probably safer than grounded assuming both systems have an EGC between all metal parts. First fault just makes the system grounded, second fault trips both circuits; sometimes one if one breaker is smaller rated or faster in tripping. Ungrounded delta and other types of systems often get bad opinions due to a lack of under standing and oldr systems which have been hacked into. A good example are those who thought or think that on an ungrounded floating system one doesn't need an EGC. Well such thing have been done, and come fault time watch the smoke as you would with a solidly grounded system absent of an EGC. In the end the non standard design or the confusing concepts get blamed, not the ignorance.
One real down side of an ungrounded system may be transient faults if the system is large, however high impedance earthing done right solves the problem.
Isolated power systems in critical care areas, mission critical infrastructure, refineries, pharmaceutical plants, hazardous facilities, bench top power supplies, electric cranes ect highly benefit from a system capable of operating with a faulted phase.
Poor choices would be lets say road way lighting. First fault probably would go unnoticed, arcing grounds from fault prone cables could easily kill sensitive ballasts and equipment to take care of that such as resistive grounding would cost way more than the benefits of a solid ground.
Grounding is individual to the desires of the application.
