Yes that is a well known bug:
http://connect.microsoft.com/VisualStudio/feedback/details/509801/
There is workaround to this for example to bind to a ViewModel's property. That would be like this:
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="{Binding Path=Width, Mode=TwoWay}" />
<ColumnDefinition Width="Auto" />
</Grid.ColumnDefinitions>
....
</Grid>
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="{Binding Path=Width, Mode=TwoWay}" />
<ColumnDefinition Width="Auto" />
</Grid.ColumnDefinitions>
....
</Grid>
And so those two grids will share the same width for first column.
This approach requires you to use proper ViewModel. :)
Edit:
I forgot the GridSplitter however the idea is to use Bindings to same property and so to provide sharing sizes... Place GridSplitter inside but most important is do not use those SharedSizeGroup tags.