It all has to do with the two things basically:
1) The speed of lookup (where integers for instance fare much better)
2) The size of indexes (where string indexes would explode)
Now it all depends on your needs and the size of the dataset. If a table or a collection has like 10-20 elements in it, the type of the key is irrelevant. It will be very fast even with a string key.
P.S. May not be related to your question, but Guids are considered bad for database keys too (16 byte Guid vs. 4 byte integer). On large data volumes Guids do slow down lookup.
NoSQL isn't a very well defined term and all the solutions that run under this name have very different features, so a lot may be possible or not depending on what exactly you are planning to do with it.
Basically you could use some of the more general solutions like maybe MongoDB or Cassandra to simply replace your current relational database. In some cases this makes more sense in others less, but it will work once your team got used to it. Certain things will be easier then, others will be more difficult and you must weight those options against each other and decide (which often enough will mean that there are no advantages big enough and the simple fact that everybody in the team feels most comfortable with relationals and SQL will make the decision easy)
Other NoSQL solutions that are more specialised are not really good candidates to replace your relational DB, like graph databases or simple key value stores. So lets from here talk mainly about those databases that are at least to some degree similar to relational databases.
Scenario 1
Where I work we have exactly this scenario, though quite more complex with a lot of different attributes per article. Some of those attributes in hierarchies like Apple -> iPad -> Air.
The data is still stored in a relational database. But: searching this in real time became a pain. With SQL it was slow and code would have been terribly complex. Selects over many tables, with the additional option to exclude certain attributes like "not blue".
In this case Apache Solr or Elastic Search are a solution. Though of course data is duplicated from the relational database.
But from here our experience with this kind of document store showed that it can handle certain problems very well and we will consider to replace part of the existing relational structure with some other kind of storage. So not the whole database where we also store all the transactional data like orders etc, but for example take out all the attribute information which can be handled much better in the aggregate like data structures of NoSQL.
Scenario 2
Difficult to say, since what you describe is most likely only a very small part of your user handling. Having schemaless storage is an advantage with many NoSQL databases. But some relational databases allow to store such data too (as long as you don't need to query it via SQL in most cases).
Cassandra for example would allow you to define column families in such a case, where your first set of attributes would be one such family and the variable attributes another one.
As somebody said: NoSQL is less about storage and more about querying. So the question is what will be the typical use case for those queries.
A typical problem would be the transactional data here. If you want to store orders, one way would be a schema where users and their orders form an aggregate (kind of user document that contains the orders as subdocuments). This would make getting a user together with his orders very simple and fast, but would make it very difficult to retrieve all orders from last month for sales statistics.
Also strengths of NoSQL solutions are that it can be easier to run them on multiple clusters if you have to work with very large datasets.
Conclusion: Both your scenarios could be modelled with certain NoSQL solutions, but I don't think that (assuming they have to run in a larger environment) they really justify a large extra effort in learning, training and implementation and maybe some other additional disadvantages because both are not specific enough to really leverage the strengths of NoSQL. At least not in that simple form you describe it. Things may become very different once some aspects you describe would be very, very prominent in your usage scenario, like in scenario one the attribute data becomes very complex or in scenario two the variable fields become the largest part of data you store with every user.
Best Answer
https://web.archive.org/web/20140831134758/http://www.dbforums.com/database-concepts-design/1619660-otlt-eav-design-why-do-people-hate.html
EAV gives a flexibility to the developer to define the schema as needed and this is good in some circumstances.
On the other hand it performs very poorly in the case of an ill-defined query and can support other bad practices.
In other words, EAV gives you enough rope to hang yourself and in this industry, things should be designed to the lowest level of complexity because the guy replacing you on the project will likely be an idiot.