In short, I would say that πρὸς and μετά are nearly synonymous in the contexts of Matthew 1:23 and John 1:1-2, respectively, but that the scope of each word is much wider in general. I try to provide some detail below.
μετά followed by the genitive case (as in Matthew 1:23) means "with" in the sense of among or in the company of. Matthew 1:23 might have just as well been translated God among us.
μετά followed by the accusative case means "after" with respect to place or time, although the former is not found in the Greek Bible (New Testament plus Septuagint). An example of the latter is Matthew 17:1:
Καὶ μεθʼ ἡμέρας ἓξ παραλαμβάνει ὁ Ἰησοῦς τὸν Πέτρον καὶ Ἰάκωβον καὶ Ἰωάννην τὸν ἀδελφὸν αὐτοῦ καὶ ἀναφέρει αὐτοὺς εἰς ὄρος ὑψηλὸν κατʼ ἰδίαν·
And after six days Jesus took with him Peter and James and John his brother, and led them up a high mountain apart.
The meaning of πρὸς also depends on what case follows it.
πρὸς followed by the genitive means something like for the benefit of or to the advantage of. An example would be Acts 27:34:
διὸ παρακαλῶ ὑμᾶς μεταλαβεῖν τροφῆς· τοῦτο γὰρ πρὸς τῆς ὑμετέρας σωτηρίας ὑπάρχει· οὐδενὸς γὰρ ὑμῶν θρὶξ ἐκ τῆς κεφαλῆς πεσεῖται.
Therefore I urge you to take nourishment, for this is for your survival, since not a hair will fall from the head of any of you.
πρὸς with the dative can convey proximity to something (e.g. "near", "by", "at", "around") as well as "in addition to". The latter usage appears only in the Septuagint; for example:
2 Maccabees 4:9
πρὸς δὲ τούτοις ὑπισχνεῖτο καὶ ἕτερα διαγράφειν πεντήκοντα πρὸς τοῖς ἑκατόν, ἐὰν ἐπιχωρηθῇ διὰ τῆς ἐξουσίας αὐτοῦ γυμνάσιον καὶ ἐφηβεῖον αὐτῷ συστήσασθαι καὶ τοὺς ἐν Ιεροσολύμοις Ἀντιοχεῖς ἀναγράψαι.
In addition to this he promised to pay one hundred and fifty more if permission were given to establish by his authority a gymnasium and a body of youth for it, and to enrol the men of Jerusalem as citizens of Antioch.
An example of the former usage would be Mark 5:11:
ἦν δὲ ἐκεῖ ἀγέλη χοίρων μεγάλη βοσκομένη πρὸς τῷ ὄρει·
Now a large herd of swine was feeding there near the mountains.
πρὸς with the accusative is much more complex. John 1:1-2 is an example of a usage that is (to your point) nearly synonymous with μετά followed by the accusative, but perhaps denoting a higher level of connection. Bauer's Greek-English Lexicon of the New Testament and Other Early Christian Literature enumerates five other usages of πρὸς with the accusative that occur in the New Testament:
- towards something; e.g. Mark 1:33:
καὶ ἐπιγνοὺς ὅτι ἐκ τῆς ἐξουσίας Ἡρώδου ἐστὶν, ἀνέπεμψεν αὐτὸν πρὸς Ἡρώδην, ὄντα καὶ αὐτὸν ἐν Ἱεροσολύμοις ἐν ταύταις ταῖς ἡμέραις.
And as soon as he knew that He belonged to Herod’s jurisdiction, he sent Him to Herod, who was also in Jerusalem at that time.
- relating to time; e.g. Luke 8:13:
οἱ δὲ ἐπὶ τῆς πέτρας οἳ, ὅταν ἀκούσωσι, μετὰ χαρᾶς δέχονται τὸν λόγον, καὶ οὗτοι ῥίζαν οὐκ ἔχουσιν, οἳ πρὸς καιρὸν πιστεύουσι, καὶ ἐν καιρῷ πειρασμοῦ ἀφίστανται.
But the ones on the rock are those who, when they hear, receive the word with joy; and these have no root, who believe for a while and in time of temptation fall away.
- relating to purpose or goal; e.g. Acts 3:10:
ἐπεγίνωσκόν τε αὐτὸν ὅτι οὗτος ἦν ὁ πρὸς τὴν ἐλεημοσύνην καθήμενος ἐπὶ τῇ Ὡραίᾳ πύλῃ τοῦ ἱεροῦ· καὶ ἐπλήσθησαν θάμβους καὶ ἐκστάσεως ἐπὶ τῷ συμβεβηκότι αὐτῷ.
Then they knew that it was he who sat begging alms at the Beautiful Gate of the temple; and they were filled with wonder and amazement at what had happened to him.
- denoting a hostile or friendly relationship; e.g Ephesians 6:12:
ὅτι οὐκ ἔστιν ἡμῖν ἡ πάλη πρὸς αἷμα καὶ σάρκα, ἀλλὰ πρὸς τὰς ἀρχάς, πρὸς τὰς ἐξουσίας, πρὸς τοὺς κοσμοκράτορας τοῦ σκότους τοῦ αἰῶνος τούτου, πρὸς τὰ πνευματικὰ τῆς πονηρίας ἐν τοῖς ἐπουρανίοις.
For we do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places.
- to indicate a connection; e.g. 2 Corinthians 4:2:
ἀλλʼ ἀπειπάμεθα τὰ κρυπτὰ τῆς αἰσχύνης, μὴ περιπατοῦντες ἐν πανουργίᾳ μηδὲ δολοῦντες τὸν λόγον τοῦ Θεοῦ, ἀλλὰ τῇ φανερώσει τῆς ἀληθείας συνιστώντες ἑαυτοὺς πρὸς πᾶσαν συνείδησιν ἀνθρώπων ἐνώπιον τοῦ Θεοῦ.
But we have renounced the hidden things of shame, not walking in craftiness nor handling the word of God deceitfully, but by manifestation of the truth commending ourselves to every man’s conscience in the sight of God.