In English you say eat soup, not drink soup. But how about Mandarin?
這個菜湯很香！ 你喝喝看！ （This vegetable soup is really tasty! You try it!)
這個菜湯很香！ 你吃吃看！ （This vegetable soup is really tasty! You try it!)
Or are both valid?
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The idiomatic way to say 'try it' in Chinese is 尝一下，尝尝，尝一尝.
You can also say 你吃一口(试试/尝尝) and 你喝一口(试试/尝尝) for eating and drinking respectively.
Your version 你喝喝看 is good too. But 你吃吃看 is not suitable for drinkings and soups. This is different from English.
As a native speaker. 這個菜湯很香！ 你吃吃看！doesn't really sound too bad since you can actually eat things in the soup. If it is just pure liquid like water, it will sound odd.
In fact, we only use 吃 in ancient times, nowadays we use 喝 more. You can simply translate all into "drink".
Obviously need to chew -> 这碗汤吃吃看/吃粥
Around the ambiguity -> 这碗汤喝喝看/喝粥
No usage of “吃汤” leads to safety~
They are both valid, see “请吃茶，吃酒”，someone even say "吃烟"（smoke ）. Angels are on your side.