Not necessarily... Depends on the application. I'm guessing, given the nature of this website, that we're looking at typical desktop computer application in which case, much of the independent testing I've seen pegs these two materials as performing essentially identical to one another. Here's a link to one test round-up where the results were identical to ArcticSilver5
The National Renewable Energies Labs have also conducted a lot of testing of thermal greases using ASTM D5470 standard testing procedures with the goal of finding good materials for use on IGBT packs used in hybrid vehicles. Completely different application, but most IGBT applications that I'm experienced with have very similar power dissipation levels per unit of area as a CPU or GPU, so the net results should be similar in terms of performance rankings between greases.
The whole report is interesting and enlightening, but unfortunately, they are comparing the Dow Corning TC-5022 instead of the TC-5121. Stick with me here, because this is still significant and I'll explain why. The TC-5022 material has a specified thermal conductivity rating of 4.0 W/m-K while the TC-5121 material Dow is only specified at 2.5 W/m-K (link to datasheet). What is interesting to note here, however, is the table on page 7 of the report. It tabulates the test results of each material tested, which includes Arctic Silver 5 and Dow Corning TC-5022. The results show that the outlandish performance claims made by the Arctic Silver folks don't come close to reality and that the TC-5022 material is superior and also cheaper. Arctic Silver makes a claim to a thermal conductivity of 8.7 W/m-K, but the test results show only 0.97 W/m-K. Unfortunately, this is typical of a lot of products aimed at general consumers who don't know any better.
The Dow-Corning products are meant for commercial/industrial applications where engineers expect the datasheets to present true information. The NREL testing confirms that Dow is claiming true performance numbers on their datasheets. The lab achieved the same 4.0 W/m-K conductivity rating that was claimed by Dow Corning. If we assume that we can safely extrapolate this truth-in-advertising with other Dow Corning products, then theoretically, the TC-5121 material should also perform better than the AS5 material.
The problem with the thermal conductivity and resistivity figures is that they don't convey any kind of sense of where you begin to reach diminishing returns on your investment. A hypothetical grease with 10 W/m-K conductivity may only net you another 1 degree improvement on your temperatures compared to a significantly cheaper grease rated at 2.0 W/m-K. At some point, the temperature rise due to the insulation created by your grease will hit a floor, that for all intents and purposes, cannot be further improved upon in a meaningful way. In most applications this point of diminishing returns is reached with grease performance somewhere between 1.4-4.0 W/m-K and it generally doesn't matter much whether it's an air or water-cooled application.
In almost all use cases, you're better off spending your money on a better heat sink with a half-way decent grease rather than some expensive, exotic, silver or diamond filled marketing hype. If you've already got the best heat sink money can buy and you still need more cooling, a good fan is your next best investment. If you're not going to get any more CFM's through that heat sink, only then should you spend money on exotic thermal grease to eek out that last little bit of performance. Most users will never need to go to that extreme unless you like living at the ragged edge of system reliability.