The incentives are very different - private garages would be very incentivized to find nothing wrong with your car and business would gravitate to those with the least checks. The government stations would not have that incentive (actually maybe incentivized the other way - to make up problems that can be waved away with money, depending on how corrupt things are there)
I'd have thought the private garages would also be incentivised to find problems - that they can then offer to fix for an additional fee.
As it is, I think most garages that offer MOTs in the UK are fair and honest, as the test is relatively strictly regulated, but I'm sure people do get ripped off.