It really depends on your workflow and personal preference(s). Logic is definitely more powerful in terms of audio manipulation, but if you are not into the user interface or the scope of your audio editing needs is narrow, the additional power is useless.
On the other hand, if you like using the traditional mixer/recorder paradigm when you record audio, you are really going about it the hard way by using Live as your main recorder. You can do it this way, but if you have Logic at your disposal, it seems counter productive.
Technically, I don't really see a lot of difference between the two in terms of sound quality; that really depends more on your interface and outboard gear.
If it were me, I would decide based on the song itself. Will the song need extensive rearranging/modularity in terms of structure? Then Live would seem to be the way to go. Are the powerful softsynths and processors in Logic necessary to complete your tune? Then the rewiring may be worth it.