To summarize from the threads already mentioned (one was started by yours truly some months ago), there's certain properties of phase ships that have to be addressed:
1.) Phase effectiveness is an inverse of ship size, i.e. smaller ships benefit more from it than larger ship
1b.)The ship system, therefore, is crucial to the effectiveness of a large phase ship
2.) Phase ships being considered "one class size up" makes a capital Phase ship something of a super-capital
2b.) This would make such a ship inherently "the best" in terms of single-most powerful vessel
None of these issues are insurmountable, mind you, but it took the Doom having a ridiculous ship system to move it way from mediocre. Now, the Doom is an S-class contender for best player ship in Vanilla. However, no matter how you slice it, a Phase Capital playing by the same rules as all the other Phase Ships isn't going to be able to exploit Phase for mobility and defense like its smaller brethren. The Doom is hardly nimble and a Capital would be even less so. Thus, a Phase Capital would need some additional help with defense, otherwise it would be vastly more vulnerable than any other Capital. Either the ship system would have to be defensive/evasive in nature, it would be a true glass cannon, or it just wouldn't operate like other Phase Ships (i.e. has a shield).
Or, more realistically, I imagine it will be a "special" ship, perhaps one-of-a-kind or at least extremely rare (like the Legion XIV). This alleviates trying to balance it against production-level Capitals and puts a bit of mystique to the thing.