As a literary artist, the writer to the Hebrews would be hard to beat. Luke is a wonderful writer; Paul's art (imho) is in his content more than his style. But the writer of 1 Peter is no piker.
Attentive readers' ears will prick up when I say "the writer of 1 Peter" instead of "Peter." The mind behind 1 Peter is Peter; I do find the amanuensis-hypothesis attractive, however. It comes from the note in 5:12—
Διὰ Σιλουανοῦ ὑμῖν τοῦ πιστοῦ ἀδελφοῦ, ὡς λογίζομαι, δι᾽ ὀλίγων ἔγραψα παρακαλῶν καὶ ἐπιμαρτυρῶν ταύτην εἶναι ἀληθῆ χάριν τοῦ θεοῦ εἰς ἣν στῆτε.
The Διὰ Σιλουανοῦ has been suggested to indicate that Peter used Silvanus as an amanuensis, to write down his thoughts, which he then reviewed and approved. At the risk of anachronism, I've been "amanuensis" to many, as has my friend Phil Johnson. My boss will give me something, I'll look it over, make reams of changes, he'll look my changes over, accept some, reject some, and out it goes.
The most fun I had as an amanuensis was when our nutcase Senatrix Barbara Boxer (—or was she just a nutcase Representative at the time? not sure) said some inane thing. That doesn't narrow it down much; pretty much every time she speaks, she says some inane thing.
But I digress.
This was years ago, and Boxer was (as liberals do) speaking for all women and saying that all women embrace abortion.
My wife, however, is a woman, and she does
not embrace abortion. But she's also a very busy woman, and though she expresses herself wonderfully, doesn't love to write. So she commissioned me to write a letter to the editor, for our local newspaper. I did so with great glee. Some of the greatest writing fun I've had was writing words to this effect: "As a woman, I am deeply offended at Barbara Boxer's implication that all women's greatest value is the freedom to kill inconvenient or imperfect children...."
What I was doing was writing what I knew my wife thought, best as I could. As I recall, she read it, said, "Yep, that's it exactly," and off it went in her name.
So the liberal critics denied 1 Peter to Peter, since it was too
polished.
Then it was said that 2 Peter couldn't be Petrine... because its Greek is too
rough!
Read both through in Greek, and the stylistic differences are undeniable. Nothing, however, requires trashing the authority of the Word as to authorship.
It is interesting, though. Peter tells us in 2 Peter 3:15-16 that he is familiar with the letters of the apostle Paul. From that testimony in
Second Peter, it's interesting to note this similarity in
First Peter:
Εὐλογητὸς ὁ θεὸς καὶ πατὴρ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ, ὁ κατὰ τὸ πολὺ αὐτοῦ ἔλεος ἀναγεννήσας ἡμᾶς εἰς ἐλπίδα ζῶσαν δι᾽ ἀναστάσεως Ἰησοῦ Χριστοῦ ἐκ νεκρῶν,
Εὐλογητὸς ὁ θεὸς καὶ πατὴρ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ, ὁ εὐλογήσας ἡμᾶς ἐν πάσῃ εὐλογίᾳ πνευματικῇ ἐν τοῖς ἐπουρανίοις ἐν Χριστῷ,
Those are 1:3 of 1 Peter and Ephesians, respectively. (Peter packs in other themes — sovereign mercy and regeneration connected to Christ's resurrection — that Paul develops in Ephesians 1 and 2, as well.) It might be fun to find other parallels, and speculate as to Peter's familiarity with Paul's letters.