Sometimes a desk can make a significant difference - but that is usually moving from a sketchily cheap large format analog desk that has not had any maintenance for 1-3 decades to anything digital.
While I normally run DiGiCo that is due to the snapshot/Macro abilities making it the brand de jour at my place of employment (keeping in mind Avid, Yamaha Rivage, SSL can do similar things).
That being said a lot of the processing I am using is in Waves land rather than DiGiCo - Why? Is it because one sounds inherently better? No.
Some of the tools offered in Waves have better functionality (dessers, dynamic EQ etc) than what is in my console, allowing me to get the result I am looking for more quickly. More importantly it can allow for the layering of compression/dynamic possibilities that are not even possible on a high end desk (well not without doing some creative routing and utilizing several channels for a single source) - however these same Waves tools with a card/host/server are available on most any desk.
When I used to own an A&H GLD I could access the same level of tools via Waves that I am using on DiGiCo - this brings a great amount of parity between products. My processing ability was the same, the difference was that DiGiCo had more inputs, macro capabilities, and more granular snapshot/scenes.
Does Waves mean a better show? No.
Waves is a giant tool box. If you do not know the tools, it will not make you a better craftsman - and even if you are a skilled craftsman an important job site where time is of the essence is not the place to learn a new tool.
Many mix engineers get themselves into trouble with plugins, as most of plugins add a small/medium amount of volume when inserted, and as a louder is perceived as better it seems better - pretty soon there are 8 plugins in the chain and while the source is louder
IT IS NOT BETTER.
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For me Waves is more about having a consistent set of tools to achieve the results I am looking for, and those are the tools I would prefer to use - that being said at the end of the day if I cannot make the sources/show sound good with the console/tools in front of me, I need to become a better mix engineer. If an X32 without any extra tools is all I have I will make the most of it, and have the best show I can - same thing if I am on "big boy" desk with a full Waves server.
Waves can be useful for one offs, but extra care needs to be taken as it can quickly become a time/focus/attention suck compared to more important elements such as band communication, cues, and macro mix adjustments -
don't miss the macro for the micro. Hint hint: speaker deployment and system linearity are a macro thing.
When I use Waves for a one off or for an event where mixdown is not a given I will be doing less in it and it will usually just be some plugins inserted as potential tools that will be added in as there is time/need.