Mishna and Gemara in Eruvin
A mishna in Eruvin (95a) says:
One who finds phylacteries outside the city on Shabbat, where they are in danger of becoming lost or damaged, brings them in to his house pair by pair by donning them in the manner in which they are typically donned for the mitzva
The Gemara in Eruvin 96ab discusses about the mitsva or not mitsva to wear tefilin on Shabbat, is it a mitsva which change through time. From this question depends an other question about duty, or option, or prohibition for a women to wear tefilin.
If tefilin are not a mitsva for women, are they prohibited or authorized to wear tefilin?
There are several opinions in the sugia. One of them is that women have to wear tefilin and tefilin is not mitsvat asse shehazman gerama. An other opinion is that women are authorized to make mitsvot without duty for them, to wearTefilin for instance.
Here is a statement from a berayta (96b)
One who finds phylacteries brings them in pair by pair, whether the finder is a man or whether she is a woman, and whether the phylacteries are new or whether they are old.
This berayta disagrees at least with the opinion that women should be discouraged from mitsvat tefilin.
Tosfot, Raavad, Rif, Rambam, Rashba.
אבל באשה לא פליגי - וא"ת דילמא משום דהוי מלבוש לאיש כדאמר בפרק במה אשה (שבת דף סא.) דתפילין דרך מלבוש עביד
Tosfot asks: Even if tefilin is not a mitsva for women, and women are discouraged from mitsvat tefilin, to wear them as mitsva is discouraged, but why not wear tefilin garment?
וי"ל דהיינו דוקא לאיש משום דרגיל ללובשן בחול אבל לאשה לא כדאמרי' התם וחלופיהן באיש דמידי דחזי לאיש לא חזי לאשה ומידי דחזי לאשה לא חזי לאיש:
Tosfot answers: Why tefilin are soon as clothes for men? Because men have a mitsvat tefilin in most weakdays. This mitsva generates an habit to see men wearing tefilin. On Shabbat we can say that wearing tefilin for a man remains a way of dressing. But if there is no mitsva for women but on the contrary this is discouraged, the tefilin are for women as men's clothing.
The Rashba in chiddushin reports in name of Raavad and Rif stated against the Berayta. Women cannot wear tefilin on Shabbat.If a woman see tefilin on public domain on Shabbat, she cannot take them even as a way of clothing because tefilin are not woman's clothing. So tefilin are not a clothes for women.
Rambam (Shabbat 19, 23) also reports the halacha mentioning men only, not women:
What should a man do when he finds tefillin in the public domain on the Sabbath? He should wear them in the ordinary fashion, placing the head tefillin on his head and the arm tefillin on his arm, enter a home and remove them there {despite that Shabbat is not zman tefilin}
The Rashba himself doesn't agree with this reasoning, but practically ruled as the Rif (and Rambam).
Magen Avraham
In Magen Avraham, OC 301, sk 54 (regarding the same halacha of a man who finds tefilin on Shabbat), the psak is also that a woman cannot wear Tefilin at Shabbat. But he adds that this shows that tefilin is a greater problem than Beged Ish, because this is a beged generally used without secular utility. And similarly a Talit Gadol. He says that a woman who walk in Public domain with a Talit Metsuyetset is Chayevet Chat'at. {as @Double AA noted in comments, the statement about Talit with tsitsiot is a consequence of habits only. If we assume that women can make as option mitsvot which are men's duty only (opinion of rabbi Yose). But the rule regarding tefilin has additional parameters, see below in note Rama siman 38}
אבל אשה אסור' להכניסה ואף על גב דק"ל דמותר לצאת בשק מפני שהרועים רגילים לצאת בהם מקרי מלבוש לכל אדם שאני נשים שהן עם בפ"ע (שבת דף ס"ב) ולכן נ"ל שאם יצאה בטלית המצוייצת חייבת חטאת אבל דבר שהוא מלבוש גמור לאיש מותרת אשה לצאת בו ועיין ביורה דעה סי' קפ"ב משא"כ טבעת לא מקרי מלבוש גמור:
CONCLUSION, it seems from the Magen Avraham that Talit and Tefilin are men's garments (as the Targum Yonatan cited by @Shalom states).
Note:
In Shulchan Aruch OC 38, 3, the Rama in name of the Col Bo says that we have to dissuade women from wearing tefilin because they are not accustomed to watch for body hygiene, not because they are exempt only.
Following the Rama, women are discouraged from wearing tefilin for the mitsva side of their wearing, so, even as clothes it is prohibited as men's clothing. But that the reason is not because they have no duty.
Regarding Talit, the reasoning of the Col Bo is not relevant. If a woman wants to wear a Talit in way to make mitsvat tsitsit, we have not to dissuade her. So talit is not men's clothing, because they are not discouraged from Talit.