I'm a 3rd year PhD student of Computer Science in the UK and I was considering joining the IEEE-CIS and/or ACM as a student member. As much as the annual memberships in both are very reasonably priced, I was wondering if there was any point subscribing to both and whether if anybody who signed up for both would recommend one over the other and suggest me some key factors to consider before becoming a member in these (or in general, other such societies).
Yes, there is a reason to be a member of both. Aside from the conference discounts mentioned by the other answers, student members get access to the digital libraries with membership in each organization. This has been the only reason that I've been a member of either for the last few years. If you're doing active research in Computer Science, you will very likely be needing access to a lot of articles from both the IEEEXplore digital library and the ACM Digital Library.
Student members of ACM get full access to the ACM Digital Library. Student members of the IEEE Computer Society get limited access to the IEEEXplore digital library and discounted access to other IEEE publications. Note that in the case of IEEE, as far as I know, this only applies to the Computer Society, not IEEE as a whole.
As O.R.Mapper mentioned in a comment, many universities provide access to the ACM Digital Library and IEEEXplore through their libraries. In my experience, however, these were more annoying/less reliable to use, at least from off-campus, though I'm sure this will vary from one university to the next. More importantly, however, at least in my case, the subset of IEEEXplore material available through the university library's subscription was not the same as the subset available through the IEEE Computer Society's student membership. The library had a journals-only subscription, while the student membership material was mostly from conferences. As such, they were actually mostly complementary.
Additionally, student members of ACM can get free downloads of much of Microsoft's software (via DreamSpark, formerly known as MSDN Academic Alliance.) This is obviously a huge benefit that pays for the ACM membership several times over with just one download. I'm not sure what's currently offered there, but I've gotten professional versions of Visual Studio and Windows 7 as well as Enterprise versions of SQL Server and Windows Server there in the past. Note that, being free, this software comes with the caveat that it can only be used for personal or academic purposes, not commercial purposes, however, the licenses don't expire when you graduate.
I was a full member of both IEEE and ACM in the past year (2014). I tend to like ACM. The CACM seems to have better quality articles and they are more CS-ish compared to IEEE which I felt are more CompEng-ish. I also prefer ACM because they send more meaningful mails and less spam compared to IEEE. For instance, ACM will send you a customized list of articles based on your interests.
I'm a fairly continuous member of the IEEE and an off and on member of the ACM. Both of them tend to bundle membership with conference fees, such that most conferences have a "registration + membership" cost that is lower than "non-member registration." As such there is rarely a point in not being a member, if you're going to a conference sponsored by the organization. I happen to go to an IEEE conference quite regularly, but not so much ACM conferences, and thus my membership trends.
Beyond that, both have nice magazines they send you (IEEE Spectrum vs. CACM), and various member services that I'm sure some people take advantage of.
Bottom line: join whoever you go to conferences with, and whether that's neither, one, or both, it's fine.
This is not a complete answer as I never cared for any of the services related to membership in either of the listed societies and never read their (in some cases, many and frequent) e-mails.
My only reason for signing up in the first place, and in fact a response to your question
I was wondering if there was any point subscribing to both
is that members get discounts on the registration fees of conferences organized by the respective society. Thus, if you attend several IEEE conferences and several ACM conferences in one year, you can save some of the money from whichever source your conference travels are paid by becoming a member of both societies.
In such a case, at least if the initial registration + the discounted conference fee is at most as high as the normal conference fee, you may also have the option to get your registration fee for the respective society reimbursed, as you are actively saving money for the funding organization.
If your academic career has taken you through any of the better universities, you may have an alumni membership that offers free lifetime access to the respective on-line libraries, even if your current institution has no agreement in place.
It's been a few years, but the ACM did offer a fairly broad selection of CBT courses, but the content of the few I looked at was fairly basic, and as full of typos as wot something I'd tapped wud contain.
Neither are UK based, so won't offer the: networking / talk / seminar options student BCS membership grants. So essentially it's a choice as to whether you'd prefer an @acm.org or @ieee.org email forwarding address and the complementry branded coffee mug, if they still offer them, you'll get for the money.