My general and mostly useless advice is to think about your story ideas in terms of their strengths, so you can pick a platform that allows those strengths to shine.
More specifically, I can say plenty about what features a parser game is good at showcasing, but I'm not really qualified to get into choice-based and other forms in the same way, so hopefully someone else will be able to cover those. (Any of the qualities I attribute to parser games may also apply to games in other forms...so, any of the following paragraphs could turn out to be not very helpful.)
To start with, in a parser game, the player can choose to examine things at their own pace. If your story trades on a rich setting or a complex backstory, you can distribute the relevant facts among various signs, books, NPC interactions, PC memories, etc., rather than delivering it via inelegant info-dumps. This doesn't apply only to fictional settings of your own creation: you can use the inherent exposition-pacing powers of the text parser to depict historical and contemporary settings in just as much detail.
Considering "setting" slightly differently, parser games are great at modeling space. Think about the experience of a Metroid game, where you try exploring in one direction, find a dead end, head back to where you were, try another direction, find the thing that un-blocks that dead end, and run back and forth and around and around until you intimately know that space—and eventually, instead of struggling against the setting, you've mastered it, and you stride across it majestically, unimpeded by any of the types of doors that used to stymie you. A parser game can deliver that same experience (as in Curses! and other old-school games with huge maps), but with walking in cardinal directions instead of jumping and shooting.
There's also a certain type of surprise that I think parser games are able to execute better than any other medium. I mean the surprise of pulling your winter coat out of storage, reaching in the pocket, and finding a $20 bill—or randomly walking off a proscribed trail and finding a quiet bench in the middle of nowhere. In other types of games, the interactable elements are easy to identify, because they're glowing, or your cursor changes into a pointing finger when you hover over them. The problem of a parser game is that the players don't always know which elements are worth their time: Should I be trying to open this door? Should I carry this pile of junk mail around forever? The magic of a parser game is that players don't always know which elements are worth their time, so authors can reward curiosity, structure jokes in unique ways, do all kinds of neat stuff.
That's all I can think of right now!
