Gigantesque is not a word as such. Gigantic is, so is the word you should use in an unfamiliar situation. Native English speakers will sometimes make up words, which are a combination of other words. Gigantesque is such a word. It is a combination of Gigantic and possibly grotesque, which would together mean very large and very ugly. A similar word that is often used here is ginormous, which is a combination of gigantic and enormous, to exaggerate the size. So - if you are writing or talking in an informal situation, where your audience are familiar with such usage, and your example sounds natural, then you could certainly use it. Otherwise - stick to dictionary words.

I would use gigantic. I can't think of a scenario where I've ever used the word gigantesque! Gigantic isn't really used commonly in English (in my experience). Huge, Massive, Large, Enormous are more common I think.