The phrase "admittedly preferred" is correct and usable in written English.
It can be used when acknowledging a preference that is generally accepted or recognized, often in a context where the speaker is conceding a point.
Example: "While both options have their merits, the more efficient method is admittedly preferred by most experts in the field."
Alternatives: "undeniably favored" or "acknowledged as better".
Admittedly, most of them preferred to migrate to the temperate regions of a select few colonies -- Canada, Australia, New Zealand and South Africa -- that soon became semiautonomous "dominions".
"Every week is going to be tough; we had to go to Catalans at some stage but admittedly we'd have preferred not to have gone in August where the players would be in a degree of meltdown with the heat in France".
Raw is preferred but admittedly not as tasty as salted.
It was admittedly not the lineup D'Antoni would have preferred, said Gherardini, now the assistant general manager for the Toronto Raptors.
This literary culture has been husbanded by a small, admittedly elite, band who prefer writing to fighting.
Citing admittedly non-existent fraud, the GOP gang reduced the number of early voting days from 14 to 8, eliminating the Sunday before Election Day disproportionately preferred, in large numbers, by blacks, Hispanics, young people and first-time voters.
Admittedly, it sounds odd to discuss intervening in 'natural ecosystems' to rescue populations from 'natural diseases' – and for these reasons wildlife managers have preferred to adopt a 'hands-off' approach in most cases, excepting when endangered species are threatened.
Grime is grimy, dirty, admittedly aggressive lyrically, but gangsters prefer glamour.
Maybe it's residual from my 20s, but I still prefer it flat – admittedly that has a more youthful look to it.
Admittedly, a reader otherwise inclined might prefer the Victorian equivalent of a car chase; you can't please everyone.
In fact, Mr. Avedon admittedly spends zero hours at the gym, preferring to skateboard, a passion that has resulted in fractured knees and ankles, among other injuries.
