Whether straight or cross head, just like other situations in life, success depends upon getting a tight fit.
Slotted head screws are good when you grind the screwdriver to fit the slot perfectly.
Cross head relies on the driver being ground to fit the screw. So you have to know which standard the screw head was made to, and buy the right driver to fit the screw head.
Phillips was one of the first. But the Philips screws are hardly ever seen these days. More common is Japan Industry Standard (JIS). Maybe the Japanese didn't wish to pay royalties to the Phillips patent owner? These have a sharper 'cross" shape. Using a genuine Phillips driver with JIS will probably strip the head. A quick test is to pick up the screw on the end of the screwdriver. If the screw falls off, the driver is not ground to match the screw.
Of course, USA has it's own (incomatible) standard cross head spec, too.
Which brings me to Bunnings Aerospace Standard. Seems the Chinese haven't heard of any of these standards. So their screws fail in many ways.