There is much discussion that goes into this debate, and everyone is entitled to their own opinion.
Personally, I have owned both sexes, and while there are certain trends with each, it would be unfair to say that one sex is "better" than the other.
It is important to evaluate each animal on its own merit.
However, let's take a look at some generalized facts that have been formulated on both male and female Chihuahuas over time.
Male Chihuahuas

• Many lift a hind leg when urinating.
  This can be problematic if you are trying to train a house broken indoor dog, or if you want him to only go on the ground.
  Most males can be house broken fairly quickly and easily.
  
• Males, especially those that are un-neutered, tend to "hump" people and other dogs fairly frequently.
  
• Males like to claim something as theirs by marking it.
  They will do this with any item in your home, especially if it's new or near the ground.
  This could be a suitcase, bed skirt, TV stand, shoes, etc.
  This is less of an issue if the Chihuahua is neutered by the time he reaches six months old.
  
• Males are typically more submissive and timid, especially if there is a female Chihuahua in the home.
  
• Un-neutered males face a risk of prostate or testicular cancer.
  
• A typical male Chihuahua is easy going, quiet, calm, and easy to please.
  
• Often are more than happy wherever you decide to put them.
  
• Generally not aggressive if they are sterilized, but can be if they are around aggressive males or are under socialized.
  
• Males are extremely smart and can easily be trained with a calm and consistent owner.
  
• Eager to please and will go out of their way to please his owner.
  
• Understand and obey basic commands very well.
  

Female Chihuahuas

• Females are more independent and bossy.
  They may assume a dominant role in the house, especially if there are males.
  More than one female in the home can cause them to get "catty.
  " However, these behaviors can be trained out.
  
• Indoor housebreaking is easier, because they squat to pee.
  
• They may occasionally engage in marking.
  Some females will mark trees and other items outdoors, but they generally won't do it inside the house.
  This is because of their alpha mentality, and thinking that they already own everything in the house anyway.
  
• Females hump things occasionally, but far less than males, and normally only when trying to establish dominance on another dog.
  Females that have yet to be fixed may hump when in heat.
  Un-neutered females will have a period every six months or so, and it can last up to three weeks.
  
• Females having not been neutered are at risk of breast or uterine cancer.
  
• Tend to be a bit more active, noisier, and also bark more than males.
  
• They are prone to hormonal mood swings, making them very temperamental.
  
• Aggression in females is harder to correct when it is due to a socialization deficiency.
  Females need to be around other animals.
  
• Females are also intelligent and take to obedience commands well, yet may need more repetition than males.
  
• They can have temporary bouts of stubbornness, meaning a refusal to obey commands they she fully understands and normally follows.
  

Keep in mind that none of these traits apply to all Chihuahuas.
Bad and good behaviors will be the extreme, with most animals falling somewhere in the middle.
In general, all Chihuahuas make great pets.
Sometimes it just comes down to a few of these generalized personality traits that are the tipping point in your decision.