Have you heard the news? The official Tumblr app finally supports tablets! But only sort of. Still, technically, you can install the app on your tablet. But be prepared: it only works in portrait mode. You know what that means, right? Yep - it's still going to suck on your 10" slate. Look at the bright side, though: it looks great on 7" tablets!
But really, there isn't much different between the phone app and the "tablet-optimized" version. Sure, there have been some slight layout tweaks; like a dedicated notification button on the bigger screen, instead of the combined panel of the phone.