In one word? No. In many more than one word? Slight. There is, however, a definite difference in the physical size and physique of male and female Burmese. I expect my male Burmese to be between 7 and 9 pounds with a thick, stocky frame, whereas my females are typically between 5 and 7 pounds with a more delicate frame and bone structure, though they are still compact and by no means skinny. But as for personality, this tends to vary more between individual cats than by gender. With that said, every once in a while I will get a male kitten / cat who has definite "swag," or swagger, which basically mean he tends to strut around as though he owns the world. Though not all males do this, I have never had a female exhibit this very particular strut.
Typically the biggest difference that I see in kittens is whether they are a dominant personality or a submissive personality, and these split pretty evenly between the genders. Both of these traits start to emerge as early as 4 weeks, when the kittens start to walk and explore their environment. The dominant kittens typically can't wait to get out of the nest, and will roam far and wide as soon as they are able. Dominant kittens love to spar and wrestle, and will typically paw at and annoy their littermates until they can get into some kind of wrestling match that they engage in with great vigor. More submissive kittens will tend to stay in the nest and will explore much more slowly, typically until they find a nice cozy place to curl up for some pets and a nap! Although they will respond to dominant littermates when "attacked," they aren't typically the instigator of the tussle. Dominant cats are typically first at the food bowl, and are much more likely to try and engage a human hand in wrestling / play biting.
Cats do have a definite social hierarchy based on the level of dominance of each cat's personality, and this should be considered when bringing a new cat into an established cat's home. Typically males will accept any new kitten regardless of dominance because if the male cat is dominant, a kitten of any gender will come in at the bottom of the social structure. If the male cat is submissive and the kitten is dominant, the kitten will assume dominance. Established females, however, can be a bit more tricky. Typically a dominant female will accept any male as she will retain dominance, even over a dominant male kitten who will eventually dwarf her in size. A submissive female will also welcome dominant or submissive males. Bringing in a new female, however, is typically NOT advisable, even if the new female is a kitten. Females typically do NOT adjust well to the addition of another female, and this "cat fight" can continue for months or even years. Though there have been times I have seen two fairly submissive females learn to get along rather quickly, this is not something I would count on when deciding what gender of kitten to bring into a one female household! If you have questions in this regard, please do not hesitate to discuss them with me in regard to your specific kitty household.
What I do not see is one gender being more affectionate / attached. Male Burmese are not more loving, more companionable, or more easy going as a GENDER than female cats as quite a few people have assumed or been told. In the same way, female Burmese are not more tempermental, prissy, shy or stand-offish than male Burmese. Most important here is that they are BURMESE, and BURMESE absolutely adore people, so male or female, I guarantee you will be delighted!