Sodas have high fructose corn syrup which is a type of sugar. One soda contains 18 packets of sugar [1]. This is far more than coffee for the average person. Now if you consider diet sodas those use aspertame as a sweetener and so it’s basically sweet’n’low packets. So on a pure sugar content perspective coffee is healthier.
Soda has been known to eat away teeth [2]. While coffee does so as well, it’s to a lesser degree[3]. So long-term physically, coffee is better.
If you consider nutritional benefits and ignore the antioxidants like you said, coffee is still mostly water and therefore can count to your water intake [4]. Soda is also water as you might imagine, it being a drink, but again, to a lesser degree.
That said, if you drink diet soda in the morning you do you. You shouldn’t feel judged for wanting to eat something in moderation. But know that coffee has proven health benefits and soda has proven health detriments. These things apply to sodas at whatever time of day.