The short answer? The one with the most well-fed nurse bees in the Starter/Finisher, and make sure it is queenless!
The truth? By all means, try running equal numbers of each - queenless and queenright finishers, if you have the bee resources to do so, but try not to make too many queens so you can't mate them all in nucleus colonies, unless you have some other beekeepers helping you. (How many queenless nuc's can you build the day before cutting out the queen cells?). Your methods and techniques will be affected by your bees, your area, the time of year, how many you are trying to produce, the skill of your helpers, etc.
Your own data will teach you far better than my California data or Michael Palmer's Vermont data, or Oldtimer's New Zealand data, or Michael Bush's Nebraska data. The gurus can give us suggestions and guidelines, but you have Swedish bees in Sverige, I have German Black bee/Italian and Africanized crosses, some people have A.M. Carnica bees, Buckfasts, A.M. Ligurica (Italians), Caucasians, Russians, other have other races, cross-breeds, and with different traits.
I wish I had a nice, neat answer in a package, but the bees always screw it up for me! Gotta stay humble.
One more point on queen quality, though - methods that do not involve transferring the larva out of her original cell (as in Doolittle Method, aka grafting) often produce superior queens to queens grafted by inexperienced grafting technicians. By superior, I mean higher % mated and accepted and not superceded as early, maybe even getting an extra year or 2 out of her. Getting 2 or 3 years out of a breeder is quite an advantage when working toward a genetic goal. These methods not transferring larva include Hopkins Method, Jay Smith / Henry Alley Method, Cell Punch Method, Mel Disselkoen's "OTS" method, the Jenter Box Method, and perhaps several others (Check out Michael Bush's website, www.bushfarms.com
for info about breeding methods). DO
breed off of each breeder queen using more than one method while practicing your grafting and getting good at it. DO
keep records on your efforts and success rates, and note the rainfall and conditions of the year. DO
assemble your data in one place for comparison, and integrate your own data into your decision-making process.
That said, once you are very skilled at grafting, you'll get lots more high-quality queens with that method, too. Nothing is faster, that is why all the commercial beekeepers and breeders use variations on Doolittle's grafting method. It does take a while to learn and get good at, though. I've been doing it for 6 years and still get some with low takes - usually my first batch of the season is embarrassingly low!
Eat Humble Pie and do it again. See, a little success puts the smile back on your face. The persistent beekeeper wins out in the long run. All the best of good luck!