Who are the sites for? Who are the intended users?
Both of these websites are for urban public libraries; therefore, the intended users are most likely a diverse population of library patrons as well as other information seekers who are either residents of, or people looking for information about, the cities these libraries serve.
The diversity of the user population is targeted in certain ways by these websites. Each site has a specific page for young users: New Brunswick has a Children’s Homepage while Hartford has different ones for Children and Teens. Hartford specifically reaches out to its Spanish-speaking population with the “En Español ” button which presents the web site (or at least most of it) in a Spanish translation. New Brunswick is reaching out to area teachers with its Teachers Homepage.
Both sites offer an array of different sources of information in the attempt to meet the needs of their various users.
What do users want to accomplish?
Since such a diverse user population would have a wide range of information needs, this question is more difficult to answer. Possibly the largest set of users are those wanting basic information about the library itself, as in contact information, address and directions, collection holdings (library catalog), services and programs it offers, policies and procedures, etc. Both of these websites address those needs well.
Others use the library website as a portal to get to other information, such as local history and community statistics. Both websites have something along these lines, New Brunswick with its "Local History and Genealogy" and Hartford with its "Community" link.
There are many other things for which users turn to a library website, and both of these sites seem to try to offer as many items of possible interest as they can.
What are the skills needed to use the site? (Basic click/scroll? Fancy menus? Downloading?) Good fit with skills of intended users?
Both sites primarily require basic clicking and scrolling, though both have roll-over menus that may be a bit more tricky. Hartford's top navigation bar uses the roll-over menus, and while there are other links on the main page to a lot of the same information found in those menus, there are also some items that seem to only be found within those menus. Here is an example:

New Brunswick only has roll-over menus on a few of its pages: "Library Services", "About Us", and "Local History and Genealogy". All three of these pages, however, only have the roll-over menu to provide links to anchors on the page, not links to seperate pages, so it is still pretty easy to find the information without using the roll-over menu.
There are items on both sites that require downloads of some kind. Hartford has a page for “program videos” on which the videos require downloading to actually watch. New Brunswick has a few links to pdf files that require downloading, pointed out in this screen capture:

PDF files are so common, however, that it does not seem too much to ask of a user to have the ability to access them, especially for the types of items that require this type of download: If you want a poetry submission form, you are most likely going to understand that you have to download it in a printer-friendly version such as PDF.
I would say that New Brunswick's site fits its intended users skill level pretty well, but wonder if some users of the Hartford site would be thrown off by the roll-over menus.
Can users instantly understand what the site is about? Understand what they can do there?
Both homepages make it clear that they are the websites for the public library: Hartford has its library logo and New Brunswick has its banner. Both sites are pretty straightforward with much of what they offer, with headers and/or images drawing users to most of the information available. Yet Hartford library's site does present some obstacles.
As previously mentioned, the roll-over menus on the navigation bar might prove trickier for some users than others, but at least the navigation bar is at the top and labeled in such a way as to make it very likely users will point their mouse towards it to find out more. The labeling for the menus, however, are not as clear as they could be, and users may miss important information because of this. The prime example is the use of the term "catalog".
The links to Hartford's catalog (both in the navigation bar up top and within the box labeled "Ask") are called just that - catalog. New Brunswick, on the other hand, incorporates the "find books" phrase to explain the purpose of the library catalog, so that users are more likely to know what they can do there. As Kupersmith discusses on his page Library Terms That Users Understand, "catalog" is a term many users do not understand, and therefore should be used with caution, or along with an explanation.
It seems that New Brunswick's site may beat out Hartford's in terms of being understandable to most users.
Does the "look & feel" entice you to stay and explore?
New Brunswick’s main page may be a bit “too busy” for some. Hartford’s may be “too bland” for others.
I personally am more attracted to the look of New Brunswick's site, since Hartford's is more white space than anything else. New Brunswick's use of color, and the pictures used on the left-side navigation area in particular, are more enticing to this user than the simplistic boxes and list of links of Hartford's site. Hartford's use of clear-cut boxes may make it more easy to focus in on the exact thing for which a user is looking, but it does not entice this user to explore.
It seems that the very basic structure of Hartford library's site may have been planned for functionality only, while New Brunswick's is meant to look welcoming. In this user's opinion, the welcoming "look and feel" is better, especially since it also functions pretty well (though that will be discussed more in the following section of this site).