If it's a work-related trip, it's a chance to do a little sightseeing on your employer's dime. If I lived in Sweden, I'd pick US because it's more expensive to go on my own. However, it's totally up to you.
Will your employer pay for a rental car? Even if they don't, I highly suggest you get one if you want to do any kind of sightseeing or shopping. It's too hard to get around both OC and LA without one, particularly for someone who doesn't live in either place. And rent the GPS, too. You can use your smartphone for directions, too, but it's illegal in California to use your cell phone while driving. If you drive, you can go pretty much anywhere if you have the time. South Coast Plaza has many different shops, including Hermes. However, they have little stock and are very crowded on weekends.
The Beverly Hills H store has much bigger stock, but traffic is horrible on weekdays, particularly during rush hour (6-10 am or 3-7 pm). If you can, stay in a hotel nearby. The Beverly Wilshire or Luxe are good options. There are lots on and around Rodeo Drive, just look for signs. If you park in the public lots, the parking is free for the first 2 hours. On Wilshire Blvd, you can get to 3 department stores: Saks, Neiman Marcus, and Barneys New York. If you dine or shop at Barneys New York (and I suggest you do), you can park in their underground lot free for 3 hours. The view from their rooftop restaurant is really nice, and they have a good mix of relatively inexpensive and higher-end foods. The weather is really nice and sunny in LA, so you can dine either inside or outside (outside tables are harder to get, obviously).
Whichever location you choose, you're bound to enjoy good shopping. Safe travels.