How should I include a list of links in my thesis?
Personally, I am in favour of adding them as references in the bibliography section.

With that said, I am from a CS subfield that is very close to the "real world" in a way that related work is almost always a motley mixture of peer-reviewed publications, books, newspaper articles, technical standard documents (such as those by W3C), and actual innovative software or websites (whose concepts were never formally published in a scientific venue), i.e. sources with a continuously varying degree of reliability. Consequently, trying to find a well-defined rule about what to add as a footnote and what to add as a bibliography reference is certain to give you headaches (and uncertain to lead to a useful and consistent result).

However, I can see a few (maybe a bit subjective) general advantages of using bibliography items rather than footnotes for links (in no particular order):


Bibliography items tend to more or less have a fixed format. Frequently, meta-information such as year of publication or author can be provided for web resources just as it can for anything else. When using a footnote, authors may be tempted to just provide the link and skip the meta-information that would be naturally included in a bibliography item, thereby foregoing both any due attribution and any information required to possibly locate the resource again, should the link die.
I have seen styleguides that generally forbid the use of footnotes (e.g. "Please do not use footnotes at all!"), but I have yet to see a styleguide that generally forbids the use of a bibliography. By not using any footnotes, your manuscript is one step closer to being agnostic of the final formatting used (and thus matches with the ideal of separating content from layout).
If the same web resource is mentioned twice throughout your document, there is absolutely no problem if the link is provided in a bibliography item, which is simply referenced twice in your text, if appropriate (e.g. if the two mentions are sufficiently far apart). If the link is in a footnote, on the other hand, things are not so clear:

The footnote can be added several times in the document. However, this means a waste of space, and it may also confuse readers who expect some new information when reading a new footnote for the first time, or who might wonder whether they are looking at a copy-and-paste error where a previously unmentioned link should be provided. Personally, I consider this "solution" downright bad style.
The same footnote can be pointed to several times. While this may be slightly cumbersome in some typesetting software, it is definitely feasible. However, it significantly increases the effort for finding the footnote (it might be on any page in the document), and the need to switch to another page than the one the reader is currently on kind of defeats the purpose of footnotes, anyway.

As a reader, I find keeping track of references, figure numbers, and table numbers that I still want to look into after finishing or while reading the current paragraph or section hard enough. There is no reason to add yet another independent list for footnote numbers.
Also as a reader, I have a certain expectation what amount of information I will find when following a pointer to additional information. For bibliography references, it is clear that the pointer points to an entire external document. For footnotes, I conversely prefer it to be clear that the pointer points to no more than one or two sentences worth of additional information (for which I do not need to search for and/or open another document).