The common difference I find in most of the old sources is that a fix is shaken and strained into service-ware containing fresh ice, while a sour is shaken and strained into a chilled glass without ice. Just about the only old source that presents the drinks as being virtually the same is Jerry Thomas. That's not surprising given that he doesn't seem to know that the difference between a mint julep and a mint smash is whether the mint is muddled or not. Jerry Thomas is great for having been the first to publish, but his knowledge often seems flawed compared to George Kappeler, William Boothby and Harry Johnson.
But, getting back to the fix and the sour, they are both technically punches - but punches that are only diluted by water melting from ice. The sour will not become more diluted, but may get warm. The fix will not get much warmer during its existence, but will become more diluted. In fact, since the water melting from the ice is lighter than the rest of the drink, it will tend to stay near the surface. This means that every sip of a fix will be rather diluted.
The choice between a sour and a fix should be decided by the drinker. Unfortunately, most bars will serve a whiskey fix when the customer orders a whiskey sour. Fortunately for those bars, the customer usually doesn't know any better than the staff.
I recently consulted for Jaragua here in Los Angeles. I wrote the menu so that the customer may order either a whiskey sour or a whiskey fix. Likewise, customers there may order their margarita as a fix, or 'up' as a proper sour.
I suggest you make or order both to find out which one you prefer.