Thank you for your response. But I'm sorry I'm still not clear about the difference between the two.
Let's assume that I'm at home talking to my wife. Since she appears to be tired from working all day, I would like to take her out for dinner instead of her cooking for us, and I say to her, 1. "I suggest we eat out tonight." 2. "I suggest eating out tonight."
In this particular situation, is there any difference between the two sentences?
(2) makes no sense in that context, Fujibei. You wouldn't advise your wife to eat out by herself or with someone else if you wanted to propose that the two of you eat out together, would you? That would be illogical. But that's what "I suggest eating out tonight" indicates in that context. You, the speaker, are not part of the eating-out situation complementing "suggest." If you wish, contrary to what is natural, to use the "suggest V-ing" structure to make a proposal in that context, then you must overtly make yourself part of the eating-out situation by using the possessive gerund subject "our": "I suggest our eating out tonight." There is NO DIFFERENCE IN MEANING OR NUANCE between that sentence and (1).