This is sort-of a hard one for me, as there are things I like about many of the different designs.
To me, it is hard to say any is the BEST design, it depends on what you like and your goals. Are you after something that is highly modifiable or looks really cool. Do you want the ability to carry lots of weight or not… How important is it to go fast? …
First round body: These are nice setups to do lots of experimenting with. My first hexapod was one of these. Mine started off life, with probably the type A legs (before the new sets…), when Jim came out with the C legs, I thought they were pretty cool looking and ordered the parts to convert mine to C. There were kits back then to allow you to add leds to the legs which also added a coolness factor. (Again mine was the Pre-current C legs). Later I converted them over to 4dof T-Hex legs as to be able to test the 4dof functionality. I again later reused the C leg parts to build a second round one, which later was cannibalized for the older quad, which then was updated to use SQ3 body with the SQ3 type legs… So you can say I went around to just about every configuration 
Which of the leg designs is best for the round ones? Hard to say. Looks wise I think the C is the most fun, But type A can be the most functional. But variations of it are also useful. Example depending on where it mounts, you may want to use an offset bracket instead of a straight one…
So for many years this was my go to platform to test things out.
Now for the Ovals, which to me each of them is very different.
Phoenix: To me this has been the coolest looking and most fun of the hexapods to show people. It can be so fluid and people react to this. However it is not a setup that can hold much weight nor would I use it to try out different mods. This was the 2nd hexapod I had. Mine started out with an Arc32 in it and only very recently did I swap this out, as I wanted to only have one board control it and kept it running as the reference robot to make sure things were working correctly.
T-Hex: Of the Oval robots, I think this one is the most versatile and is fun as it work with. It is great to experiment on with electronics as you can setup multiple boards and have access on the two sides. (Currently has RPI and SSC-32u) Also there was ideas that you could build this as a Quad or Hex (although never saw as quad). The initial leg design for the 3dof was setup to make it easier to construct to have contact sensors in it, which some of us were going to try to use for Terrain Adaptation. The 4DOF leg version is fun as it looks like some storm trooper… But cost, power requirements… Not sure how many people went for that option.
A-Pod: Don’t have - Kåre’s original version is really cool looking, especially with the body parts. Note: I have an Orion robot that is similar to the A-Pod. Again a really cool type of robot, but to really make use of it, I personally think you need a more advanced Input device than a PS2 and a lot of dexterity, like Kåre with the DIY remote.
What should the new ones have? A lot of this probably depends on other stuff, like what type and shape of servos, What type of electronics. Are you going to have some Arduino or Linux versions, or are you going to only concentrate on tethering it to your computer. …
Body Shape: Round is nice for some things as it can move more or less equally well in most directions, however the Oval ones do usually move better going foreword and backward. Personally for new stuff I would probably go more with Oval shapes.
Leg design: Mostly 18dof unless good reason to go to 24. Foot sensors? Maybe depends. What capabilities do I have with the servos. With Dynamixel servos (likewise with Orion), I have some control over the servos and some feedback. So depending on how the legs are done may be able to sense things. With Orion servos (with their Orion Shield) you can tell the system to stop a servo/leg when the force exceeds some value. With AX Servos, I know Kåre had some luck experimenting with when the leg is coming down, configure the servo to only output so much force, so it will stop when it hits something, when you go to the next step you can ask it where it is and/or tell it to now hold… So again don’t know the answer.
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Again this is the hard one. Would be nice to have a few different ones…
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Material - Not a big one for me. Metal is strong and the like, but can also short electronics…
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other factors:
a) I hope you still have the ability to customize, example change between a few different angle brackets, or maybe different C brackets or the like to make custom legs.
b) Good to have expansion capabilities, like add on decks
c) One thing that is nice about Trossen Hex/Quad, is that their Coxa servos don’t rotate inside the body. I especially like this with Lipo batteries as for example the Orion robots legs are like rotating daggers, that could easily slice a battery or cables, which really scare me with Lipos. So far I have not put lipos on Lynxmotion robots (except for an LifePO4)
d) If servos can run well on Lipos, design to make it easy to remove Lipo for charging and storage.
Probably can go on and on, but probably enough for one post.
Kurt
That is if you are saying all legs inline with each other like BH3, for some reason never interested me. I think Alan has had better luck making it walk by then offsetting the leg initial positions. However if you are talking about something like T-Hex where the brackets that is different… Also hard to say one way or another. Example: What is the shape of the Trossen PhantomX? Not really Oval, not really rectangular… Also not necessarily saying they are the most esthetically perfect look either…