There's no such thing as "twice as good" when it comes to hardware. Your best bet is to determine your budget. Then you can look at the charts and see which card works best for what you want to do with it.
For something relatively inexpensive, the Radeon HD 6670 which can probably bought for $60 after rebate. It will crush the old 8400GS. There's also the Radeon HD 7750 which is probably about 40% - 50% faster than the Radeon HD 6670 and is generally around $90 after rebate at Newegg.com.
This card is for someone that will never use it. He doesn't even use the 8400GS to it full potential. All he does is watch films and browse the internet. And plays the odd HOG, or point and click adventure. Nothing that even requires the use of a gaming card.
But, he wants to upgrade it, he upgraded his case, he's bought a fan controller, he's even now talking about upgrading his motherboard, cpu, and ram.
So all that I need is something that is "somewhat" better.
The Radeon HD 6670 is a little too expensive. Do you know anything cheaper? This is after all a completely pointless upgrade, there's no need to spend more money then is necessary.
Another advantage to these newer cards is better hardware acceleration in web browsers something most users can benefit from. anything much lower is most likely not even worth buying, then again neither is buying for no reason at all.