I could be wrong, but I don't think getting one negates your ability to get the other. (they're both Chase cards, so that's why I mention that)
That being said, the Disney Visa card, specifically the one all these invites are for (which is the no annual fee one), is a bit superior to the Sapphire, for a few reasons:
1) You only need to spend $500 for the Disney Card to get your reward, not $4000 like the Sapphire card.
2) The Disney card gives you get a physical $200 gift card (and another $50 if they are still doing the "add an authorized user for an extra $50" promo), not miles or points or reward dollars that you will need to deal with later, this is stuff you use in the park.
3) No annual fee for the Disney Card. Sapphire wants $95 per year starting your second year
4) If you use one of the invites provided by the folks here, you help THEM get $50 in Disney Reward Dollars (which is really the Disney Card's version of points ) Sure there's no additional help to your bottom line, but... it's a nice thing to do and all. Just to be clear, THEM getting $50 does not cost you anything, they just get a reward for the "referral."
5) The Disney Card is specifically geared toward Disney stuff and activities, so you get a discount on some tours, merchandise (gift shops) and dining while in the park (For example, the Keys to the Kingdom tour is 15% off using the Disney Card)
Now, if you do a nice financial two-step and/or depending on your spending habits, you can certainly make the Chase Sapphire work for you, for example paying for your vacation using the card will likely yield you the full $500 reward. But the Disney Card seems a lot less effort from the get. And with no annual fee and only needing to spend $500 to get your reward, there's really no risk at all that you will have a monstrous balance to deal with later.
So I would say, if your credit can handle it, maybe consider getting both and/or even more cards. Additionally, there are other cards out there that have a few nice rewards (some are mentioned in the spread sheet). The best thing you can do is compare all the cards against each other and see which one works best for you.
EDIT: one other thing, if you do get the Disney card, it takes a few weeks for your gift card(s) to get to you, so factor that in with your "prep for vacation" schedule. Don't be like me and end up not getting your card until two nights before you leave! lol