I tried both for some time. I started using a bottling bucket as you describe.
Then, to avoid extra oxidation and to save some time, I tried to bottle directly from the primary, pouring the boiled mix of water and sugar (or DME or original worth) into the primary and then into the bottle. The clarity was nice at the start and then (depending from the yeast flocculation) exceptional after some months (from 2 to 6). Here is the con: I opened some beers that are more carbonated than others. Even if I poured the mix at the start of the bottling process, to let it mix with the beer without agitating, I think that I had more sugar in some bottles than in others. It's difficult to say for sure, but I still have this feeling...
I think I will go back to the bottling bucket again and make some more tests...
Cheers!

Piteko