From a maintenance personnel point of view:
(Note - I am not an FAA qualified maintenance person, but did some reading on their system. I am more versed on EASA)
EASA (With regards to Cat B1 - mechanical certifying technician) - The B1 license holder supervises / assists in carrying out the task at hand done by "fitters" (the person actually getting his hands dirty). The fitter does not have any legal certification privileges, but his name is appended on the paperwork as the person performing the job (for accountability within the company only, not legal), then signed by the B1 licensed holder in the Certifying personnel column, who holds the legal responsibility.
FAA - The A&P mechanic is "licensed" by the FAA. He is the person actually getting his hands dirty, & signs for the work done & is accountable legally. If the work is deemed critical, an Inspector (who is actually an A&P person with at least 5 years experience & passed the Inspector exam by FAA) will counter check the work.
From my experience working in a hangar environment, I much prefer the FAA system. That is because in a hangar environment, many tasks are being done at the same time. In the EASA B1 system, you will be supervising fitters who do not hold any legal responsibility, but they're doing the job, & you are supposed to supervise them (could be lots of them at the same time doing different jobs).
In the FAA system, the A&P mechanic does the actual job is legally responsible for it. More task oriented.
Please correct me if I am wrong in any of the above.
Any A&P mechs, A&P Inspectors & EASA B1 licensed guys out there agree/disagree with my statement above?