Just for comparitive purposes, our group plays a lot of games and we used to keep records of wins and losses. The Priest has never won and never come close in our group. That said, we use the 40 new characters I created (available at TalismanIsland), so each character is played infrequently.
Still, the Warrior, Elf, Dwarf, and Wizard account for about half of all victories, even with around 60 characters in the mix, suggesting they're advantageous in some ways (let's not start in on the Elf, his victories in 2-3 player games speak for themselves and he's got his own thread). Again, we've played well over 60 games now (I stopped keeping track for a while) and the Priest has never survived past the first 20 rounds of play, let alone winning. Here's our scoresheet.
1. Archon/6/Dwarf
2. Brights'/5/Warrior
3. University/2/Elf
4. University/2/Ghoul
5. Brights'/4/Warrior
6. Brights'/4/Thief
7. Brights'/4/Sorceress and Warrior standoff (Poltergeist+Healer)
8. Brights'/2/Troll
9. Brights'/3/Dwarf
10. Washington/5/Warrior
11. Duffy's/3/Minstrel
12. Duffy's/3/Gnome
13. Bob's/4/Pixie
14. Brights'/2/Monk
15. Brights'/2/Troll
16. Brights'/3/Elf
17. Brights'/2/Warrior
18. University/2/Shaman
19. University/2/Warrior-Mage
20. Washington/2/Prophetess
21. Washington/2/Wizard
22. Washington/3/Monk
23. Brights'/3/(Unlucky Gambler+)Barbarian
24. Brights'/3/Enchantress
25. Brights'/6/Druid
26. Brights'/3/Troll
27. Duffy's/3/Dwarf [switch to revised edition, 4.5]
28. Duffy's/4/Minstrel
29. Duffy's/3/Warrior
30. Brights'/2/Drunk Farmer
31. Brights'/2/Chasm Horror
32. Brights'/2/Boatman
41. Duffy's/2/Wizard
42. Brights'/4/Riverborn Shifter
43. Brights'/3/City Doctor
44. Washington/6/Knight
45. Brights'/2/Dark Cultist
(then many many games played, DC wins about 1/2 of them, nobody kept track)
With The Dungeon
46. Brights'/2/Gypsy
47. Brights'/5/Swashbuckler
! He finished with Str 15, Craft 6 and hills kills included a Giant and 2 Dragons. Sadly, with the Gladiator packing 7 Followers for +7 in battle, even Str 15 couldn't touch him.