Critical has a better damage consistency and you would have the ability to not only break but to deal damage to others as well during WoE, this means you could very well defend and break at the same time. The advantage of this build is that you can skimp on a lot of stats and add a lot more vitality that adds on to more health points, thus surviving longer. This build does not require any Dex as critical ignores the flee rate of all players. With all the new items and the valkyrie weapon for Assassin Cross and with the new addition of the Blessed Ring for Assassin Cross, you don't really need to add Luk at all.
Thanatos build breaker is a different build all together, the damage is from average to high and it does not have a steady flow of damage consistency. However this build has the added advantage of the Double Attack skill that increases it's damage per second output, thus increasing your chance of breaking the Emperium, reason being the more damage per second you deal the higher the chances of you getting the last hit. You would also have to deal with having lesser health points compared to Critical build assassins and you would also not be able to hit other players as the usual build for a Thanatos build have only enough hit to hit the Emperium and not players with decent flee rate. With that being said, even without Thanatos card, you could still break with a Double Attack build so long as your damage that you are dealing to the Emperium is high enough to level with the other builds. It is very much possible, tested and proven.
Hope this clears out to everybody about the differences between the two build, I would not help out on giving you a build as it's rather personal to me. What I can share with you is that most of the advise given on this thread are of somewhat relevant and of use. Good luck in breaking. Cheers.