Transferring your H1-B is much easier than getting one..
You can apply to a new green card via the new employer (or any potential employer too). Once you get through to the I-140 stage of your second GC again - provided that the new job is one similar to your previous one - you can use your same place-in-line in the GC as before.
The green card application can get stuck in the bureaucratic backlog for any number of reasons - for years. These delays messes up with your peace of mind in ways you can probably imagine. Internet is full of horror stories about these things. This prevents people from changing jobs, or making any long term plans about buying a house etc.
It is a long-standing request from many people stuck in GC backlogs to not have them go through the _unpredictable_ re-application process, when they switch jobs. This was hinted as part of President Obama's Executive Action on immigration reform.
In a memo[1] dated 11/20/2014, Jeh Johnson (Secretary of Dept. of Homeland Security) stated:
As you know, our employment-based immigration system is
afflicted with extremely long waits for immigrant visas, or
"green cards," due to relatively low green card numerical limits
established by Congress 24 years ago in 1990.
...
To correct this problem, I hereby direct USCIS to take several
steps to modernize and improve the immigrant visa process.
[1] Executive Action: Support High-skilled Business and Workers - http://www.dhs.gov/sites/default/files/publications/14_1120_...
[2] USCIS Seeks Comments on Proposed Rule Affecting Certain Employment-Based Immigrant and Nonimmigrant Visa Programs - https://www.uscis.gov/news/uscis-seeks-comments-proposed-rul...
[3] http://www.regulations.gov/#!docketDetail;D=USCIS-2015-0008
Main problem with H1b is low wages and lack of mobility - lose your job and you're out.