I would go for the second one near Old Street station. The area is much more trendy, vibrant, diverse and popular with young people. It is also slightly closer to LSE and other parts of central London. It is safe, but due to it being a popular nightlife location you should be careful at night if walking around on your own.
The first one is in Shepherd's Bush which is an area that's good for shopping due to the big mall situated in the middle of it. It is a lot less interesting though and there's not much to do at night. Lots Again it is safe but there are some notorious social housing areas nearby (e.g. White City estate) that are a bit deprived and might be scary to walk through at night,