The weak negative correlation between the Freedom House findings and HRW's focus is all because of Israel. The -0.12 correlation turns into +0.31 if Israel is taken out of the calculations.
Thanks to commenter RuthieofAmerica and my own efforts, I added the statistics for the Americas, most of Asia/Pacific, and Europe. (No sub-Saharan Africa at this time.)
There is one other area of the world where one can see a similar heavily disproportionate focus, and that is the Americas. The correlation between the two is a very weak 0.07, but if you take out the United States from the equation, it turns into a much stronger 0.42. This is because HRW mentions the US far, far more than any other country, over 14,000 times according to Google, more than double the next country I have statistics for (Pakistan.)
The correlation for Western Europe was 0.47 and for Asia/Pacific 0.27 (I didn't include some of the tiny island nations.) For Eastern Europe it is 0.25.
Keep in mind that the Freedom House score is between 2 and 14.
Using a very rough calculation, one can see that compared to Freedom House's numbers, HRW is most biased against the United States (14700/4), France (3710/2), Israel (3940/3), the UK (1740/2), Hungary (1400/2), Australia (1330/2) and Canada (1280/2.)
On the other hand, HRW does not give nearly the proper attention to South Ossetia, Brunei (258/11), Laos, Turkmenistan, North Korea, Oman (328/11), Qatar, and Bahrain, with countries like Algeria, Libya (1240/14), Yemen, Cuba, the UAE and Syria (1510/13) not far behind.
In the middle, with what appears to be a proportional focus by HRW, we see Turkey, Saudi Arabia, Cambodia, China and Iran.
Here are the numbers I have so far, in rough order from HRW under-reporting to over-reporting. (My formula was a simple one: HRW mentions / (FW score - 1). )
Country  |     HRW  |     FH  |    
| Northern Cyprus | 9 | 4 | 
| Nagorno-Karabak | 101 | 10 | 
| SouthOssetia | 198 | 13 | 
| Dominica | 18 | 2 | 
| Abkhazia | 197 | 10 | 
| Paraguay | 115 | 6 | 
| Tajikistan | 249 | 11 | 
| Brunei | 258 | 11 | 
| Laos | 356 | 13 | 
| Moldova | 178 | 7 | 
| Turkmenistan | 404 | 14 | 
| North Korea | 413 | 14 | 
| Oman | 328 | 11 | 
| Mongolia | 113 | 4 | 
| Bosnia-Herzegovi | 228 | 7 | 
| Nicaragua | 294 | 8 | 
| Qatar | 456 | 11 | 
| Armenia | 411 | 10 | 
| Bahrain | 460 | 11 | 
| Latvia | 108 | 3 | 
| Macedonia | 276 | 6 | 
| Trinidad/Tobago | 168 | 4 | 
| Montenegro | 230 | 5 | 
| Guyana | 250 | 5 | 
| Haiti | 512 | 9 | 
| Panama | 129 | 3 | 
| Azerbaijan | 655 | 11 | 
| Belarus | 792 | 13 | 
| Algeria | 787 | 11 | 
| Kazakhstan | 799 | 11 | 
| Singapore | 649 | 9 | 
| Bolivia | 408 | 6 | 
| Uzbekistan | 1070 | 14 | 
| Albania | 412 | 6 | 
| Guatemala | 730 | 9 | 
| Kyrgyzstan | 933 | 11 | 
| Libya | 1240 | 14 | 
| Yemen | 999 | 11 | 
| Bulgaria | 315 | 4 | 
| San Marino | 106 | 2 | 
| Romania | 319 | 4 | 
| Suriname | 320 | 4 | 
| Cuba | 1070 | 11 | 
| Lithuania | 107 | 2 | 
| Antigua/Barbuda | 450 | 5 | 
| Estonia | 115 | 2 | 
| Honduras | 839 | 8 | 
| UAE | 1200 | 11 | 
| Liechtenstein | 122 | 2 | 
| Syria | 1510 | 13 | 
| Bangladesh | 767 | 7 | 
| Dominican-Republi | 384 | 4 | 
| Iceland | 130 | 2 | 
| Jordan | 1300 | 11 | 
| Morocco | 1060 | 9 | 
| Monaco | 272 | 3 | 
| Tunisia | 1530 | 12 | 
| Kuwait | 1130 | 9 | 
| Puerto-Rico | 142 | 2 | 
| StVincent/Grenadi | 294 | 3 | 
| Malaysia | 1040 | 8 | 
| Kosovo | 1210 | 9 | 
| Taiwan | 308 | 3 | 
| Burma | 2030 | 14 | 
| Luxembourg | 157 | 2 | 
| Slovenia | 161 | 2 | 
| Georgia | 1140 | 8 | 
| Thailand | 1330 | 9 | 
| Ecuador | 871 | 6 | 
| Grenada | 356 | 3 | 
| Peru | 738 | 5 | 
| Belize | 371 | 3 | 
| Vietnam | 2070 | 12 | 
| Egypt | 1930 | 11 | 
| Jamaica | 776 | 5 | 
| Lebanon | 1450 | 8 | 
| Iraq | 2170 | 11 | 
| Afghanistan | 2510 | 12 | 
| Nepal | 1610 | 8 | 
| Serbia | 718 | 4 | 
| Colombia | 1440 | 7 | 
| South Korea | 483 | 3 | 
| Finland | 260 | 2 | 
| New Zealand | 262 | 2 | 
| CzechRep | 265 | 2 | 
| Brazil | 833 | 4 | 
| Turkey | 1400 | 6 | 
| Croatia | 569 | 3 | 
| SaintKitts/Nevis | 287 | 2 | 
| Greece | 602 | 3 | 
| Malta | 308 | 2 | 
| Costa-Rica | 311 | 2 | 
| Barbados | 318 | 2 | 
| Cyprus | 320 | 2 | 
| Saint-Lucia | 326 | 2 | 
| Ukraine | 1340 | 5 | 
| Argentina | 1010 | 4 | 
| Bahamas | 339 | 2 | 
| Saudi Arabia | 4140 | 13 | 
| Slovakia | 345 | 2 | 
| Andorra | 347 | 2 | 
| El-Salvador | 1490 | 5 | 
| Cambodia | 4110 | 11 | 
| Venezuela | 3320 | 9 | 
| Mexico | 1680 | 5 | 
| Poland | 420 | 2 | 
| China | 5080 | 13 | 
| Austria | 430 | 2 | 
| Russia | 4300 | 11 | 
| Italy | 869 | 3 | 
| Uruguay | 436 | 2 | 
| Japan | 964 | 3 | 
| Iran | 5730 | 12 | 
| Denmark | 548 | 2 | 
| Indonesia | 2370 | 5 | 
| Switzerland | 597 | 2 | 
| Ireland | 602 | 2 | 
| Pakistan | 5710 | 9 | 
| Sweden | 721 | 2 | 
| Belgium | 747 | 2 | 
| Norway | 768 | 2 | 
| Netherlands | 997 | 2 | 
| Portugal | 1020 | 2 | 
| Chile | 1070 | 2 | 
| Germany | 1080 | 2 | 
| India | 4400 | 5 | 
| Spain | 1140 | 2 | 
| Canada | 1280 | 2 | 
| Australia | 1330 | 2 | 
| Hungary | 1400 | 2 | 
| UK | 1740 | 2 | 
| Israel | 3940 | 3 | 
| France | 3710 | 2 | 
| USA | 14700 | 4 |