The COCA (Corpus of Contemporary American English) shows American English having a preference for level of safety over safety level by 3.5 to 1. Records in the BNC (British National Corpus), by contrast, show their use as being more or less equal.
We may speculate on why that might be so, but my own intuition suggests to me that the two expressions would be used in different contexts, with level of safety having a more specific reference and safety level a more general one. For example, the BNC has this extract illistrating level of safety:
Thermostat is the first level of safety. Set to operate at around
60C to 65C. Energy cut-out is the second level of safety and is
set to operate at 85C to 90C to turn off the boiler or other source of
heat. Temperature/pressure relief valve is the third level of
safety and will discharge water (through a second tundish into a
safe and visible place) if the temperature of the water reaches 95C.
Compare that with this, illustrating the use of safety level:
But the pound found a safety level and was firm against the mark
and the dollar.