A long, long time ago in a galaxy far, far away, I was a kid who was miserable in her piano lessons. I learned that the piano is both a percussive and stringed torture device… 
Seriously, though, it is both, and perhaps uniquely so. But I would like to raise the secondary aspect of intonation as a basis for considering musical instruments.
In any non-percussive instrument, the note has to be shaped (or found, or created, however you care to phrase it) by the musician, working through and in tandem with the gross mechanics of the instrument. So with brass instruments (e.g., trumpet), you adjust the slides to tune the instrument before the performance. When playing, you have to obviously have to use the correct fingerings to hit the notes, but working the valves properly does not ensure good intonation or even clean attacks (and stops) on the notes; for that, you still have to maintain the correct embouchure of the lips and tongue.
I’ve never played a woodwind, but my understanding is that the general principle applies to their instruments as well; although the mechanics (blowing through a moistened reed vs. buzzing into a mouthpiece) are quite different.
Perhaps someone with experience playing a stringed instrument can comment on the challenges of maintaining proper intonation when fingering the strings on a violin, viola, cello, etc.
Now, contrast that with the experience of playing the piano, where the one thing the pianist really doesn’t have to worry about is intonation. (Once the piano is properly tuned in the first place, that is.) I can assure those without piano experience that the experience of playing piano is very much a percussive one. The player concentrates on striking (and releasing) the correct keys correctly (hard/loud vs. soft/softly). The challenges of striking the correct combinations of notes as musically as possible is the compensating difficulty of an instrument on which playing “in tune” is not a concern.
On a bit of a tangent – although this may stand to be corrected by someone more knowledgable, it’s my general understanding that it is the way a piano sounds when a note is attacked that, more than any other aspect, defines the characteristic sounds of various piano brands. Yamaha grands and baby grands have a reputation for having a “brighter,” “cleaner” (or, derisively, more “plinky”) sound than other more traditional-sounding piano manufacturers, whose pianos have the quality of having softer, more muted (or, derisively, “muddier”) note shaping.
And correct me if I’m wrong on this, but didn’t the advent of digital recording and CDs shift (if only temporarily, for the first decade or so) the classical recording industry in favor of those pianists whose playing styles emphasized the clean, precise attack (and who often chose to record on those bright-sounding Yamahas) – resulting in a wave of classical piano albums that stood, collectively, as a revision of the muddier, comparatively muted sounding recordings of old? [O.K., end of tangent]
But if the piano seems on balance to be percussive from the player’s perspective – whether playing a Yamaha or not – I can understand why it seems more like a stringed instrument from the listener’s perspective. The piano has a timbre arguably more akin to other stringed instruments than to that of the percussive, woodwind, or brass, particularly during the sustained part of the notes. And certainly, the balance of the sound of a piano is in the sustained duration of the notes, beyond the initial fraction-of-a-second bite at the beginning of each.
There’s another musical aspect worth considering, too, in the ability to sustain and vary the dynamics and intonation of a note. String, brass, and woodwind instruments all have a pronounced ability to carry a note at full strength for a long period of time (well, several bars, anyway). But consider the actual sound of a piano note: you have the initial “attack,” followed by a potentially long fade (sometimes sustained by use of the sustain pedal). The piano note is loudest at its inception and its intonation is fixed; by comparison, one of the great freedoms enjoyed by the non-percussive classes of instruments is the ability to tinker with the dynamics and even intonation of a note after it is first played.
[self-spoofing of pedantic tendencies follows]
I would like to offer, none too seriously, a final point of observation in the debate over the classification of the piano as percussive v. stringed. I call it the “Don Martin Non-Musical Catastrophic Full-Bodied Application,” in which the piano – be it regular-sized, baby grand, or gloriously full-grand – is depicted by that esteemed late “MAD Magazine” caricaturist most typically in the moment of its being precariously transported.
Most typically, said piano is being raised to or lowered from an elevated or walk-up apartment (or perhaps educational institution) in a pronouncedly urban setting (e.g., New York City). Said piano is being relocated by means of a none-too-trustworthy mechanical apparatus, such as a pulley or perhaps winching device, which is operated by a couple of – variously – blue-collar, under-educated, uncouth, unalert, inattentive, posterior-scratching, underwear-hitching, yawning, belching, or girl-watching morons.
The moment of crisis, inevitably, is signalled by the introduction of the oft-put-upon “Fester Bestertester” character. Said Mr. Bestertester will be, say, strolling along the sidewalk, happily minding his own business, inconguous and oblivious to the grand piano straining its pulley ropes, some fifty (or 500) feet above.
One should not be surprised if Mr. Bestertester should be suffering from a mild medical malady – say, a bump on the noggin or a painfully ingrown toenail – and may even be on his way to the doctor’s office at that very moment. One shouldn’t even be shocked if the star-crossed Mr. Bestertester tarries unexpectedly for a fateful moment (to pick up a nickel, say), while under the penumbral shadow of said piano (which, like many an immigrant to NYC, is yearning to breathe free), far overhead. Rest assured, only at that moment will the piano, accidentally and stupidly loosed from its bonds, be abused in the most percussive way imaginable. To say nothing of the abuse that will immanently be visited upon Mr. Fester Bestertester…
[/pedant]