When it comes to an all rope rode, there are two good choices and one bad choice.
The first good choice is three lay nylon rope. This material has about 20% stretch and considerable strength for its size. It is also the cheapest of all the rope options. Being three lay, it is very easy to splice and also very easy to repair. Should a segment become chafed, it can be repaired by performing a mending splice. Should you need to add length to your rode, you can always carry it out by performing a short splice or long splice. The possibilities are endless when working with three lay nylon!
The disadvantage of three lay nylon is that it is succeptible to chafe and the section of rope that attaches to the shank of the anchor will be the most chafed section of the entire rode. Careful inspection will let you know when it is time to repair this area and prevent the loss of your expensive and precious anchor!
The second good choice is megaplait nylon rope. This rope is made by weaving many smaller strands of nylon together in a tight and integral pattern. This line is considerably more expensive but at the same time, considerably more resistant to chafe than three lay nylon. It doesn't have as much stretch as three lay, but it is still enough to absorb the shock loads presented by a well buried anchor.
Splicing megaplait is very tedious, as there are many small strands to deal with and it takes considerable patience to complete a splice. Repairing megaplait is also rather tricky, so it is fair to say that it is not as friendly to the user as three lay is, but still a very good option if you can afford the line.
The last option, which is the bad option for an anchor rode is any kind of double braid line. Double braid line does have an outer core that would protect the core from chafe, but the core is impossible to inspect from the outside to evaluate its strength and it does not have anywhere near the needed stretch characteristics of regular megaplait or three lay. This means that the shock loads on the rode will be higher, putting the rode at much greater risk to cause damage to the ground tackle system and possibly snap the rode.
While all rope rodes are an option for an anchor rode, they are far from the ideal setup. The rope is rather light and will not provide the catenary curve needed to create the lateral pull the anchor requires to set and hold properly. All rope rodes require much longer scope to achieve the same holding power and are at risk of chafing through and breaking.
If you anchor for a few hours on a weekend when the weather is nice, a rope rode will serve you well. if you plan on cruising and spend almost every night on the hook, it will be worth the investment into an all chain rode.