Well assuming that Commodore never messed up in the 80s and 90s with regard to the Amiga (possibly by not losing millions on PC clone making), and having a wider range of computers available to cover more market areas through the 90s and get ongoing repurchases and upgrades ...
I would presume that they both would have had to change CPU architecture in the 90s. Amiga was meant to go PA RISC at the high end, but possibly that would have changed in the long run to PowerPC. I imagine Atari would have gone PowerPC if the ST/Falcon had continued, or MIPS. The 90s had so many different architectures!
Still, if they were both PowerPC in the early part of this decade, the cumulative marketshare of Apple, Amiga and Atari would have been a higher impetus for PowerPC CPUs to be improved sooner and better than they were ultimately. So PowerPC could still be around in desktop computers, in a similar manner to x86 CPUs today, perhaps a bit ahead even.
However the Amiga and Atari would be using the standard buses - PCIe, graphics cards from ATI, NVIDIA, etc, and so on, rather than custom chipsets. I think custom chipsets would have been dead by the end of the 90s, or even earlier. AmigaOS/Workbench would be similar to modern Mac OS X or Windows 7 in function, style, etc. It may have gone through a Mac OS -> Mac OS X transition period to make up modern in terms of memory protection and so on, but it would have remained AmigaOS.
