Define "safe"? Will any transformer configuration make it safer for a human to touch a live circuit? No, absolutely not. This has ZERO to do with personnel protection. Will one secondary configuration cause equipment to be damaged? Not likely. The issue is what do you want to happen IF there is a ground fault condition, and by the way, NOT the equipment experiencing the actual fault, but rather the REST of the facility.
If you have n UNGROUNDED delta secondary, the first ground fault changes you to having a Corner Grounded Delta and the REST of your facility carries on like normal as the ground fault current is cleared by a LOCAL protective device. The thing is though, the NEC now requires you to have EITHER a Ground Fault Monitoring system on this, or use a Corner Grounded Delta, which means you have ALREADY lost that first benefit, and a GF Monitoring system is not cheap.
So the more widely used alternative now is the Resistance Grounded Wye secondary system in which the Wye point (Neutral) of the secondary is connected to Ground with a Neutral Grounding Resistor. That too serves to limit the current flow during a ground fault elsewhere in the system, again so that the protective device CLOSEST to the fault can clear BEFORE an upstream device does, one that might be covering a larger portion of the facility (or the whole facility), causing major costs if it trips.
So again, in NEITHER scenario is the secondary configuration intended to make anything "safer", it's purpose is to help prevent one small problem from becoming a catastrophe.
