Edit 7: Updated for Patch 4.0.6, which added 11 new dig sites: 7 Tol'vir in Uldum in Kalimdor, 2 Nerubian in Northrend, and 2 Nerubian in Eastern Plaguelands in Eastern Kingdoms. You should now find ~62% more Tol'vir sites in Kalimdor now and ~30% more Nerubian sites in Northrend. I'm going to just call Pre-375 Pre-450 for the sake of the table.
Well I haven't seen any other topic with conclusive evidence, just random assertions like "NE sites are more common in Kalimdor", which while true, left me wondering about numbers. So while this data isn't exactly hard to come up with (Wowpedia + Excel spreadsheet + If statements), I still thought I'd share the conclusions. Specifically, the data comes from http://www.wowpedia.org/Archaeology#Zones_and_dig_sites and http://www.wowpedia.org/Dig_site.
These are percentages describing what percent of the continent's dig sites are of that culture. A 25% next to Troll at Northrend would mean that 25% of the dig sites on that continent are Troll. A higher percent indicates a higher chance of getting that dig site on that continent, so that is obviously more desirable and is helpful information if you are hunting a specific culture's rare.
Here's a picture of a shiny table.
Dwarf
There is only 1 Dwarf site in Kalimdor compared to 18 (post-450) or 14 (pre-450). No contest on this one, but here are the percents anyway.
Eastern Kingdoms (pre-375): 28.57% (14/49)
Eastern Kingdoms (post-375, pre-450): 27.45% (14/51)
Eastern Kingdoms (post-450): 32.73% (18/55)
Kalimdor (pre-450): 2.08% (1/48)
Kalimdor (post-450): 1.45% (1/62)
Verdict: Eastern Kingdoms (All skill levels)
Fossil
After the removal of the Vashj'ir dig sites, I am forced to recommend Eastern Kingdoms post-450 for Fossil fragments. Before that though, they're exactly even.
Eastern Kingdoms (pre-450): 26.53% (13/49)
Eastern Kingdoms (post-375, pre-450): 25.49% (13/51)
Eastern Kingdoms (post-450): 23.64% (13/55)
Kalimdor (pre-450): 27.08% (13/48)
Kalimdor (post-450): 18.84% (13/69)
Verdict: Kalimdor (pre-450) and Eastern Kingdoms (post-450)
Night Elf
There are only 2 Night Elf dig sites in Eastern Kingdoms, and just a few more than that in Northrend. On the other hand, over half of Kalimdor is Night Elf.
Eastern Kingdoms (pre-450): 4.08% (2/49)
Eastern Kingdoms (post-375, pre-450): 3.92% (2/51)
Eastern Kingdoms (post-450): 3.64% (2/55)
Kalimdor (pre-450): 62.50% (30/48)
Kalimdor (post-450): 50.72% (35/69)
Northrend: 13.79% (4/29)
Verdict: Kalimdor (All skill levels)
Troll
Troll relics are also in Northrend, so here's a three-way comparison.
Eastern Kingdoms (pre-450): 40.82% (20/49)
Eastern Kingdoms (post-375, pre-450): 39.22% (20/51)
Eastern Kingdoms (post-450): 36.36% (20/55)
Kalimdor (pre-450): 8.33% (4/48)
Kalimdor (post-450): 5.80% (4/69)
Northrend: 17.24% (5/29)
Verdict: Eastern Kingdoms (all skill levels)
Draenei
This one is easy because there is only one location, but I'll list it anyway for completion sake and just for fun.
Outland: 53.57% (15/28)
Verdict: Outland
Orc
See above.
Outland: 46.43% (13/28)
Verdict: Outland
Nerubian
In addition to upping the number of Nerubian sites in Northrend slightly, Blizzard added two Nerubian sites to Eastern Plaguelands, requiring 375 Archaeology, of course. I'm not going to create a new column in the table just for 375-450 Archaeologists, so you'll just have to live with the numbers being here!
Eastern Kingdoms (post-375, pre-450): 3.92% (2/51)
Eastern Kingdoms (post-450): 3.64% (2/55)
Northrend: 24.14% (7/29)
Verdict: Northrend
Vrykul
Only one possible area for these.
Northrend: 44.83% (13/29)
Verdict: Northrend
Tol'vir
Only one possible area for these as well, but luckily, Patch 4.0.6 has nearly doubled the amount of Tol'vir sites in Kalimdor.
Kalimdor (post-450): 23.19% (16/69)
Verdict: Kalimdor (post-450)
And just for kicks, in their most populated areas, Tol'vir and Nerubian are the two rarest races to get things from. Luckily, there are only two Nerubian artifacts of any value, so you won't have worry about them very often.
Also, I figured I'd use this space to point out this: My post is based on assumption, like most things in the world. This assumption is that the the number of dig sites of each culture is directly proportional to the chance the dig site is selected. As far as I can tell, this assumption appears to be accurate though. The results appear to justify the assumption (low Tol'vir/Nerubian rates, etc).