There’s a practical difference between eating and sleeping in that tzar can make sleeping impossible so that you would accomplish nothing by lying in the Sukkah, but the same rain would only render eating uncomfortable.
People have pointed out that you have to eat a kazayis in the sukkah on the first night in rain, but you don’t have to sleep in it. This isn’t a proof that eating is more strict than sleeping. In fact, one could point out that a person only has to eat in the sukkah for achilas keva m’ikkar hadin, while for sleeping he has to do so even for a nap. I’m not making the inference that sleeping is more strict, but I’m am showing that you can make it sound like either one is more strict by pulling halachos out of context like that.
By the way, you probably aren’t being mevatel anything by not eating in the sukkah on the first night in rain either. It’s a machlokes rishonim, and I believe the mechaber doesn’t even mention it (I would have to look again to be sure). If it were for sure a mitzvah d’oraysa, we would say a brachah.