I prefer F!Robin over M!Robin in character design, voices, and overall potential impact in the storyline. I certainly don't think M!Robin is bad in any way, but when I compared the two gendered options during Awakening's speculation, I found myself gravitating more to F!Robin because of how interesting her default design looked. It also gave me the opportunity to finally play as a female main character in Fire Emblem that wasn't just a glorified side character (i.e. Lyn in Eliwood's and Hector's stories, which were the true story of FE7, and Micaiah in RD), or was sharing it with the arguably more important male main character (Celica in Fire Emblem Gaiden, Eirika in Sacred Stones). Even though I knew that Chrom would be seen as the face of Fire Emblem Awakening, I felt that Robin would be the character most crucial to the storyline and to the player, and it shows.
I find it interesting, because I usually preferred playing as the male gender when given the option to customize. It was something that I developed from playing RPGs at a young age, back when I never even thought of role playing into original characters, so I never really considered trying it out until recently. Now, I tend to alternate between genders when I feel that 1. That particular gender could potentially better resonate with me in the storyline, and 2. When I feel as though that particular gender is criminally underused in the setting or the series (this almost always applies to females). For example, in Fallout 3, I played as the girl because I thought the Lone Wanderer worked well as a sheltered, hesitant woman thrusted into the dangerous landscape, forced to search for her father, while gradually growing into a capable and dynamic warrior who's able to defeat hordes of raiders and ghouls alike because she's just that good. In Fallout: New Vegas, I opted to play as the male because from the start, I imagined him as a gruff, grizzled cowboy mercenary who doesn't like nonsense of any sort, and yet is disturbed by some of the customs of the locals, like slavery in Cesar's Legion.
So nowadays, I usually go one way or the other.