I'm a relative newbie to diving. I started with my first training book and then got a nice paper logbook that I neglected to put my training dives in and then I started using Subsurface because I'm much more comfortable typing than writing and I often can't read what I handwrote later anyway (I should have been a doctor!) and then I got my very first dive computer (Mares Puck Pro) that has its own dive log and now I am taking an SSI skills update course that is pushing the SSI dive log. I haven't done anything in person with SSI yet, so I can't talk to the instructor directly.
So... I think Subsurface is what I want to stick with. Does it matter that I have 32 dives in Subsurface and only 27 in my paper book? Do I really need to maintain a paper book or can I just print off a summary from Subsurface if a dive operator or instructor wants to see something on paper? I know I can import from my computer to Subsurface, so I don't really need to use the Mares log. This class is my first experience with SSI at all, but I've seen some posts of people wanting to switch all their logging to SSI. Is this just a matter of preference or will I actually need to keep the SSI log if I take more classes with SSI in the future? My open water was NAUI and my Advanced Open Water was PADI. It seems like every area I live has a different organization that the dive shops are part of, so my future classes might be SSI. I don't love the training content with SSI (which seems heavily and annoyingly peppered with ads for SSI stuff) but it might be all I can find locally.
TL;DR: Can I ditch the paper book and SSI logs and just do everything in Subsurface?
I actually keep logs three ways:
1. Traditional Paper logs - for me this is a reflective process where I can document the experience of the dive, how I felt, keep details on where my weights were placed and how much. I can also add context around the dive, for example, that we went to a pub after the dive and it was hilarious when so-and-so laughed so hard beer shot out his nose. In short, my log is the qualitative, narrative dive log that harbors the emotion and experience of the dive. I stopped logging briefly an probably lost 20-30 dives that way, but other than that, I am very religious about this as well. Also as an instructor, when I log teaching dives, it is a written record of the skills completed with students during a dive and gives me additional information on my students' training record (and records in case of - god forbid - legal liability). Students also sign my log as well, initialing their skills.
2. Electronic logs - these largely are created by my dive computers and data is captured during the dive and then synched with a cloud-based portal where I can add additional data about the dive. I use Shearwater computers as well as Divesoft.
3. Excel - I keep detailed quantitative logs in Excel. Much of this duplicates data from dive computers but I also track SAC, RMV/SCR, weighting, and other metrics. I then can look at averages, trends, and other data that can be tabulated and used for dive planning. For example, if I were diving in West Palm Beach, and I know that my average SCR during a drift dive while wearing a 5mm wetsuit and carrying a single tank with Xl bs of lead, I can predict what my likely gas consumption will be for the dive and create a very detailed dive plan.
As for your other question - generally whether logs are reviewed by anyone in real life prior to a class, dive trip or other. The answer is yes. And for this, I think paper logs can be useful to have. Prior to my divemaster (and then during my instructor training) I needed to share my logbook and my Course Director reviewed every single dive. I have been on a charter too that asked for logs to show experience in the environment (I was a new customer and didn't dive often with them). For me, I will also look at a students logs sometimes, because I want to know whether their dive experience is 100 dives in a quarry or whether the experience is more diverse. Sometimes, I want to see these if a student comes to me and I am not familiar with them. Also for some courses, for example, some specialties, a student can get credit for dives from their Advanced class - but if I don't know what they did, I can't verify it.