Everything eventually rots in strong sunlight.
Go with the rubber; it insulates better anyway, even after a 10 years of sun. YMMV.

There are much greater questions here than just the expected lifespan of an insulation material.

Why is the pipe being insulated?
Insulation alone will not protect an outdoor line from freezing.

What kind of material is the pipe?
PVC,CPVC and PEX all deteriorate when exposed to direct ultraviolet exposure which explains why the ASTM standards state that all synthetic pipe materials must be protected from direct exposure to sunlight.

The pipe runs along the side of the house, from an original external faucet to an extra one that was installed later. For hard freezes, it also has a valve and drain at the upstream side.

The pipe material is copper. Actually my main concern is that, even after draining the exposed pipe, it will still get cold and conduct heat upstream back to the original faucet, causing the original faucet to freeze. My hope is that the insulation will help to minimize the amount of cold that is transferred to the external length of pipe and then to the main faucet which it is connected to.

"My hope is that the insulation will help to minimize the amount of cold that is transferred to the external length of pipe and then to the main faucet which it is connected to."

Without a source of heat insulation wil not make much difference.
The connection should have been made in a heated area or below frost depth.
As long as you can drain the water to a level below the frost depth it is very unlikely an empty pipe will move enough heat to cause a problem.

You need to keep in mind that insulation only slows the flow of heat, it does not stop it.

In recent years there has been a big trend and sadly in some areas a code requirment to install "Frost proof" hydrant type hose bibbs. This then leaves the homeowner with the false illusion that the pipe cannot freeze and break. In reality, nothing could be further from the truth.

First of all, note that the faucett is listed as "Frost Proof" not "Freeze Proof". There is no such thing as a "Freeze Proof" faucett. In fact, the expansion of freezing water will rupture galvanized iron pipes and even a cast iron engine block, which explains why you put antifreeze in your car.

A basic law of physics states that heat is a form of energy and cold is the absence of energy in the same manner as light is a form of energy and dark is the absence of light energy.

When a pipe, such as a hose bibb is projected through a wall and exposed to the outdoor enviroment the heat energy in the faucett body and the water in the pipe is radiated to the air. As the heat radiates the faucett and the end of the pipe is now cold. The heat energy on the inside section of pipe now radiates toward the cold section and as it continues the pipe will get progressively colder inside the house as well.

Generally it requires a very cold external temperature and considerable time for the pipe to cool sufficiently to be a problem inside the wall thus a frost proof faucett will provide a moderate protection for the occassional overnight freeze, but in a northern climate where we experience sub-freezing temps for days or months often the outer 24" to to 30" of the pipe will cool below freezing. For this reason most plumbing codes in cold climates require us to install a "line stop & waste valve" at least 3' inside the heated portion of the structure. For winterization the line stop is turned off and the hose bibb should be left open to permit any residual water in the line to flow out. All the pipe on the outside of the line stop should be pitched downward at 1/4" per foot to insure the line will drain.