Use of infinite/-ing: to have someone do something or to have someone doing something

I have a question regarding the use of infinite/-ing (or past participle?) in the following sentence. Which one is correct between

"Firms often have some of their executives sitting on the board of competitors."

and

"Firms often have some of their executives sit on the board of competitors."

? If both forms are wrong, could you suggest a correct form? If both forms are correct, could you kindly say it in an answer?

Solution 1:

"Firms often have some of their executives sitting on the board of competitors." This construction implies a state of being. It's similar to saying "Executives for firms often sit on the board of competitors."

"Firms often have some of their executives sit on the board of competitors." This construction implies that firms intentionally place executives on competitors' boards, similar to saying "Firms often request that some of their executives sit on the board of competitors."

Both forms are correct, but you need to pick the version that fits what you're trying to say. One other note "board of competitors" feels awkward. If what you mean is "the Board of Directors of a competitor" then you should probably phrase it as "competitors' boards" or "competitor's board".