In the first movie and the anime series, Mewtwo's voice clearly indicates that Mewtwo is male. In the 16th movie, Mewtwo appears to be female. It was then shown that that Mewtwo can mega evolve into Mewtwo Y. From this, is it possible that there are two Mewtwos, where the male is Mewtwo X and the female is Mewtwo Y? I know that in the game, Mewtwo does not have a gender, but this is from the anime's perspective.
The evidence overwhelmingly indicates that there are two Mewtwos. Firstly, in Genesect and the Legend Awakened, Mewtwo didn't give any indication of recognizing Ash, even though it should have known him from the movie Mewtwo Strikes Back. This indicates it was a different Mewtwo. Secondly, it has its own backstory in the special episode Mewtwo: Prologue to Awakening. I haven't seen the special, so I couldn't say for certain whether the events therein completely contradict the idea of there being only one Mewtwo, but what I've read indicates that the second Mewtwo's creators survived, which contradicts the fact that the first Mewtwo killed its creators.
The evidence for either Mewtwo having a gender, however, is nearly nonexistent. You submit the voice actor/actress for each Mewtwo as evidence of its gender, but I would contend that this is very insignificant. Especially for animals (or Pokémon), an actress can play the role of a male character and an actor can play a female character. Shaymin from Giratina and the Sky Warrior is an example to consider. In the English dub of the movie, Shaymin's voice actress used a more masculine voice for when Shaymin turned into its Sky Forme, but used a feminine voice for Shaymin's Land Forme. This demonstrates that the voice acting isn't a good indicator of a Pokémon's gender.
Furthermore, the anime rarely reveals the gender of any Pokémon. For example, just look how few of Ash's Pokémon have confirmed genders. Of his Pokémon from Kanto and Johto, only the genders of Pikachu (male), Bayleef (female), and Butterfree (male) have been confirmed. Notably, his Pokémon from Unova have the highest percentage of confirmed genders. This is because his Snivy knew the move attract, the effectiveness of which depends on the Pokémon being of the opposite gender.
And there you get to my point: The gender of a Pokémon is only revealed in the anime when there is reason to. The gender of Mewtwo really doesn't matter, and there is no reliable information from the anime as a result. If we're just going by the anime, we don't know the gender of either Mewtwo.
Edit: In the Black and White: Adventures in Unova and Beyond episode To Catch a Rotom!, Professor Oak confirms that Rotom is genderless after an attract move by Iris's Emolga fails. The existence of genderless Pokémon in the anime is likely an indicator that the anime follows the games in this matter, and that Mewtwo is also genderless.
I did some research and it appears that there are actually two different Mewtwos, as you suggest. I know this sounds a bit outlandish at first, but it is mentioned and supported in numerous different sources.
In game: genderless
Real mewtwo from the first movie: male
New mewtwo from genesect movie: female, apparently
From Pokemon Database:
The original Mewtwo, created by team rocket (First Movie & Mewtwo Returns), was a male.
This is the moody Mewtwo you know best.
The second Mewtwo appears in Genesect and the Legend Awakened and is female.
There is no real evidence for exactly who created this Mewtwo, but it may have been another team following Giovanni's original plans. It could also have to do with the "multiple parallel universes" mentioned to exist in ORAS.
If this were to be the case, this Mewtwo would have been created at abut the same time in about the same circumstances, but was born a female and may have never met Ash.
In general, it appears that the movies can sometimes operate within different timelines of the regular anime, so these multiple parallel universe theories can exist separately.
From the Bulbapedia entry for Mewtwo, it states that Mewtwo is genderless, but Bulbapedia refers to the games and not the anime/movies.
You can also watch this video, where a semi-popular YouTuber discusses the gender of Mewtwo (and reaches the same conclusion that there are two Mewtwos).
https://youtu.be/cYPCHyP-9hw Watch the first 30 seconds of this video. It confirms that there are 2 different mewtwos, and they have met. It’s Cannon, as it was a special on Cartoon Network a few years ago
The Mewtwo in the first movie and in Mewtwo Returns is confirmed male - from Giovanni saying "Good Boy" when Mewtwo willingly goes into the trap made by Giovanni. And the more masculine voice just helps validate this, but the fact that Giovanni stated him as a "boy" for me validates he is a male.
As for Mewtwo in the Pokémon the Movie: Genesect and the Legend Awakened - it is a different Mewtwo. It is voiced by a woman in both Japanese and English dubs, but there is no actual confirmation of its gender by pronouns or etc. We "assume" it is a female but there is no real indication of its gender as there was with the first Mewtwo. Also, this Mewtwo is clearly a different Mewtwo by the choices of voice actors, and also the fact that Ash recognized it as Mewtwo, but the Mewtwo from the Genesect movie didn't recognize Ash. Ash also 'acknowledged' it was a different Mewtwo in the Mewtwo x Genesect Movie. This Mewtwo can also mega evolve to Mega Mewtwo Y at will, which the original Mewtwo from the first movies never could.