So, each person experiences 1 second ticking as normal, but if you were to look at both watches together, one would be much, much slower than the other.
This has actually been proven by syncing atomic clocks and putting one on the space shuttle. The one on the shuttle comes back showing a time a few milliseconds less than the one on the ground.
They'll be very slightly less productive in that situation because time has slowed down for them. For everyone sitting at home, time moves 1 second every 1 second. For passenger in Bugatti, a stopwatch says 0.99999* second for every 1 second felt by everyone else. So what feels 1 second to the passenger is 1/0.99999 = 1.000001 to everyone else. Hence he's actually slower.
When person A finishes (say a week later) and comes back, he'll find that person B finished "a long time ago." That is, person B finished, and then waited till person A came back (say for a year, depending on how fast person B was going).
What happened? Time went at different speeds for each person. They each took a week from their own point of view!
Which one is right? Both of them. Thats what relativity says. There is not one thing called "time" but that its "relative" (hence the name).
So, if your going to choose to hire one of them... you'd hire person B (assuming your business is on Earth).
If two people program 60 lines of code per hour, one does so in a spaceship traveling nearly the speed of light and one does so on earth... after 1 year/365 days/8760 hrs they make a report on their progress and they don't have the same results? If a watch ticks every second, the faster you go the slower it ticks? Why? How?
Will people be buying a 2100 model Bugatti, hiring a driver, and working in the passenger seat to be more productive?