This is an old post, but since everyone still searches for and reads them I wanted to add my two pence - I compare the science libraries as of 10/2019.
Both libraries are about 5 minutes walk from each other.
The Birkbeck library is in the shadow of Senate House, one of the iconic buildings in London, but is in quite a modern purpose built complex.
UCL library is hidden away down a pedestrianised side street of buildings which are practically devoid of any character, and it is not purpose built - you will need to open a lot of doors and climb a lot of stairs to go from one area to the next, all of this creating noise.
The library reception area is perhaps more impressive at UCL, a mix of old and modern, at Birkbeck, the library reception is much smaller and you normally have to tailgate someone in. That said, there is an open-door librarian's office on floor 1 in addition. I did like the décor at UCL in the rest of the building, it is old school, but the building did not lend itself to being a library, in my opinion- at a guess, it seems like it used to be a hive of classrooms and it was converted.
Birkbeck is quiet in the quiet areas, possibly due to more mature people, more people who have worked all day and just want to get things done and go.
UCL library is not as quiet, full of people whispering, there to chat, who know that it disturbs others but they just don't care, because they care too much about themselves (read lack of maturity). That was happening on all floors.
In terms of comfort, Birkbeck library has sofas and private/group cubicles in some areas, with meeting rooms for groups, I didn't see any at UCL but I might have missed that?
Privacy is much higher at Birkbeck, you have a proper metal screen separating your desk if you sit at the window, whereas at UCL they have this odd little orange flimsy plastic thing which is about 10cm high separating you from the person opposite and nothing to your right or left. Bad for concentration and good for weirdos. I'm also not sure you could sit facing out by a window at UCL. At any rate, this was a quite pleasant thing to do at Birkbeck, although they have concreted over the grass lawns they used to have and still show in their brochures...
At UCL you know which floor you are on, because the architecture is different, at Birkbeck every floor is pretty much the same.
There is a private restaurant on the top floor at Birkbeck. UCL has restaurants open to the public at street level.
In terms of lighting, Birkbeck library has far more natural light as both sides have huge windows, modern on the one side and old sash windows and at least one balcony on the other. This gives much more of a feeling of space and calm.
When I went to UCL science library, floor 1, 3 and 4 smelled very strongly of BO (sweaty people who don't change their clothes, bath or use deodorant). This was despite several windows being ajar and it being a cool October.
Very honestly, when one UCL student joined me in the lift, I had to close my nostrils.
At Birkbeck, (I went 5/6 times each), there are no obvious smells - no food is allowed, people are relatively cleaner, the air con works quietly.
Both libraries were fairly crowded, but not unduly bad. Both libraries are mostly all foreign students, perhaps more so at UCL (a lot of Chinese).
Both libraries have tons of computer workstations.
At UCL, when you go to the engineering section, the door slams every time someone comes in and all the so-called 'engineers' look up when you walk in. Had to laugh at their non-interest.
Both libraries had an equally good selection of books, for science I had a notional memory of UCL perhaps in addition, having some older (or out of date) periodicals and books in specific (read 'niche') subject areas. I think parts of these books could be used to study, or read for interest, they were perhaps just part of the collection.
Overall, I expected more from UCL and was quite happy with Birkbeck (science books compared only).