When choosing a frame, likely the most considered factor is Motor Placement; Where the motors are on the frame in relation to each other.
There are those that place a lot of weight in motor placement, and there are those who look to other factors first. The purpose of this post is to go over as many placements and their purposes as possible. Feel free to skip to the most relevant part as it suits you.
Let's start with X.
X was the original quad-copter design, before FPV was so much as popular. It's purpose at the time being that having the motors at equal distances was necessary to achieve balanced flight, before programming and algorithms played a larger role in flight characteristics.
Since then the H quad has come and gone, and the X has returned again for flight characteristics. Not because the flight controllers can't keep up with other configurations, but because they simply seem to play nice with each other. When it comes to racing and tuning, the X configuration is simply easier to deal with and has very linear flight characteristics.
Next we'll go over the "Classic" H quad, and cover benefits of a well designed H quad.
Probably the most classic and well known H quad is the Blackout 250, better known as it's copy the ZMR 250. This is a great example of a simple configuration where the motors were spread farther apart on the Roll axis, there is no specific science to How they are moved in this case. But at this point in time, and to present of course, flight control firmware's have no problem compensating for this change. The noticeable difference is of course flight characteristics and tuning. Tuning an X quad will noticeably easier than a quad configured in an un-proportional H. As for characteristics, you will probably notice that because of the lack of leverage in the Pitch axis, the stability in forward flight will be less while turning and rolls will be almost Too accurate.
On the subject of tuning however, we have to consider the ever popular Alien H quad.
When they were released and so many avid hobbyists flew them for the first time, they were considered one of the easiest quads to tune and the best flying quad of it's time (all 8 months ago or so). Well for those of you that read their original RCGroups thread, you'll know that they stated "The 3:4:5 proportion simply flew better in testing with consideration to the body mass on the pitch axis." and that it would be easier for the FC to calculate because of the equal proportions. Many manufacturers did not follow their lead with that discovery, but instead moved on to "Pure X quads" which have their place of course.
Somewhere in between this mess of "perfection" we have Dead-Cat quads.
A Dead-Cat is basically an a-symmetrical quad, like the Shen Drones Shrieker. Two motors are closer to each other, front to back. Surely it'd be possible to do it side to side, but to what end I'm not sure. This frame design proves that, unless you can really tell the minor differences in characteristics, any frame can and probably will fly just fine.
Last, but certainly not least, is the "Stretched X" quad.
The newest contraption is the Stretched X configuration. The name is a little misleading, if you take an old H quad and turn it sideways, you get a "Stretched X". Some manufacturers are measuring the stretch in degrees from center, but I think we will find soon that the 3:4:5 triple will prove to fly the best.
As for characteristics, the idea of the stretch is that the leverage over the Pitch axis is greater than an X or H quad, making it very stable in forward flight. While the short distance in the Roll axis makes it roll faster and turn sharper.
In conclusion, unless you fly every day or hate tuning, Almost any frame will fly pretty good. Especially with modern flight controllers.
Feel free to write any questions or comments.