Pyrotechnical's answer already covers why people are unhappy with the change, which is mostly unrelated to the new license itself and more to do with how SE announced the change of license on existing content.
As for the changes themselves, Tim Post's announcement of the change on MSE directs people to this blog post on creativecommons.org for a summary of the changes:
We proudly introduce our 4.0 licenses, now available for adoption worldwide. The 4.0 licenses — more than two years in the making — are the most global, legally robust licenses produced by CC to date. We have incorporated dozens of improvements that make sharing and reusing CC-licensed materials easier and more dependable than ever before.
We had ambitious goals in mind when we embarked on the versioning process coming out of the 2011 CC Global Summit in Warsaw. The new licenses achieve all of these goals, and more. The 4.0 licenses are extremely well-suited for use by governments and publishers of public sector information and other data, especially for those in the European Union. This is due to the expansion in license scope, which now covers sui generis database rights that exist there and in a handful of other countries.
Among other exciting new features are improved readability and organization, common-sense attribution, and a new mechanism that allows those who violate the license inadvertently to regain their rights automatically if the violation is corrected in a timely manner.
The blog post also directs readers to this article for a more in-depth explanation of the improvements in the Creative Commons Version 4.0 licenses. Rather than quote the entire text of the article, I'll just list the headers and quote a relevant sentence or two:
- A more global license: "The 4.0 licenses are ready-to-use around the
world, without porting."
- Rights outside the scope of copyright: "Other rights beyond copyright
can complicate the reuse of CC-licensed material. [...] Version 4.0
addresses this challenge through an open-ended but carefully tailored
license grant that identifies categories of rights that could (if not
licensed) interfere with reuse of the material."
- Common-sense attribution: "The licenses explicitly permit licensees
to satisfy the attribution requirement with a link to a separate page
for attribution information."
- Enabling more anonymity, when desired: "Version 3.0 included a
provision allowing a licensor to request that a licensee remove the
attribution from an adaptation, if she did not want her name
associated with it. Version 4.0 expands that provision to apply not
only to adaptations but also to verbatim reproductions of a work."
- 30-day window to correct license violations: "All CC licenses
terminate when a licensee breaks their terms, but under 4.0, a
licensee’s rights are reinstated automatically if she corrects a
breach within 30 days of discovering it."
- Increased readability: "The 4.0 license suite is decidedly easier to
read and understand than prior versions, not to mention much shorter
and better organized."
- Clarity about adaptations: "The BY and BY-NC 4.0 licenses are clearer
about how adaptations are to be licensed, a source of confusion for
some under the earlier versions of those licenses.
Hopefully this provides a decent summary of the differences in the license between versions 3.0 and 4.0. Note that Stack Exchange is using CC BY-SA 4.0 specifically, so some of the changes listed above may not be relevant to it. (I'm not a lawyer, but I hope you found this helpful.)