They're both grammatically correct and accepted.
For me though, and if you would like to dissect the nuance between them,
Both of them mean a "person to whom thought or action is directed"
But object emphasizes:
"a person seen as a focus for feelings, thought etc."
ex. an object of affection/ contempt
While subject:
"one who experiences or is subjected to something"
ex. the helpless subject of their cruelty/ ridicule
Can one eat lunch? Because, lunch is not food itself, one cannot eat it.
I think lunch does not only refer to the time one eats the food, it can certainly refer to the food. And merriam-webster agrees with me:
1: a usually light meal; especially : one taken in the middle of the day
2: the food prepared for a lunch
So, analogous to meal, breakfast, dinner, on can certainly have it and eat it.
In contrast, this doesn't work with cake:
You can't have your cake and eat it.
It seems that with meals, which we can have, the meaning has shifted (or grown) to include also the specific food to be served at the meal, and because of that, we can also eat a meal. But food can be either had or eaten, where having the food does not imply eating it. So the extension of meaning only works in one direction, from meal to food, and not from food to meal. That said, on can order a steak by saying I'll have the steak, please, but strictly speaking, the fact that you probably intend to eat it once they give it to you is only implied.
Best Answer
I wouldn't say it's wrong, just unusual. Commonly heard are "I consider it important", I judge it important", "I deem it important", and I can't see any reason why you couldn't say "I see it important". It's just that people don't. They say "see it as important", "regard it as important". I don't know why one collection of verbs needs a following "as" and another doesn't. But go with common usage unless there are compelling reasons for doing otherwise.