Personally, I can pretty much go either way. Both have their downfalls.
For geldings, it is the fact that boys will still be boys, and some of them take FOREVER to get over the fact that they have been gelded. At the time, they are probably the better choice for newbie riders because they tend to be gentler with people.
For mares, it is their attitude. Just like human females, we have attitude and intuition and we are not afraid to show it. Not to mention, when they are in season, we must understand that life is hard on them because they have got all the silly boys chasing them.
However, though I love both, I would much more prefer a mare. I own a GREAT gelding, and at the same time I have met a gelding who still had the testosterone(sp?) attitude of a stallion. With the two mares I own right now, I believe that I can understand them better, and that they understand me.
But, all in all, it really depends on the horse. Some geldings and mares will be great, some will just have attitude and be "alpha-ish"
Red Money Maker (Red) - 2004 Sorrel QH Gelding