Red, brining does make a difference in taste and texture of the poultry, especially the white meat. The salt "denatures" the protein, increasing water retention. A little salt goes a long way with poultry. What you are showing above is about 2 cups of salt, 2 cups of sugar, and a gallon and a half of water. The very first time I brined a turkey a LONG time ago, I used something similar and it was almost inedible it was so salty. You might want to start with half that amount of salt and sugar.
One BIG word of warning. Check the label on your turkey. If it says it has been injected or enhanced with a salt solution of 8, 10, 12, etc percent, it has already been brined by the supplier. I smoked a pre-brined, 19 lb turkey this past weekend and did not brine it again. It was juicy and tender.
Brining a pre-brined won't do anything to the moisture, but you can add flavor by cutting WAY back on the salt and sugar, say to 1/3 cup each, then putting your preferred spices in the brine. I'll inject that brine into the breast to get the flavor profile I want.
Fruit juice is a wonderful brine for pork. Apple doesn't add much flavor. Orange and lemon juice combined (50/50) to make what is called "sour orange" is a fantastic pork brine. Look up Cuban style pork on Google to get an idea. My favorite is tart cherry juice.
Brining beef is called Corned beef, pastrami, etc, and it uses curing salt. Marinades are a better choice for beef in my opinion. There are also injectable bases that use phosphates to help beef retain moisture, like Butcher BBQ injection. They are pricy but have a strong following.
Hope that helps.
Ray