My understanding of the issue is that it less about running multiple tasks at the same time, it is about how aggressively it closes apps that haven’t been accessed for a while.
Not had any issues with having music playing while on the internet, ebook reading or texting/ calling. There is more than enough grunt under the hood!
However, if you use the recent apps button and scroll back to select an app that hasn’t been open for a while, the you will find it has been closed and it will reopen. Can’t give you an exact length of time before it closes though. It works fine flicking between a few open apps, say between a game, email and browser, but once an app has been dormant for a period then it will be closed. This obviously doesn’t affect apps running all the time in the background like gmail – these will carry on with whatever sync period you have set.
Not really a big issue for me, even if it has been closed they will tend to open pretty quickly. If you are the sort to flash custom roms, then I think some of the roms over on XDA have been modified to keep apps open/ in the memory for longer.
Happy to be corrected if this is on the wrong track!