As someone who serves as the Dean of our Online program here at Westminster, and currently teaches the same classes in both residential and online format, I have a unique position to evaluate what is actually happening over a range of students. I can't speak for other people's residential and online programs, which range from excellent to terrible, though I have taught at other institutions over the past 30 years. It's pretty clear that there are distinct advantages and disadvantages to each mode of learning that should be taken into account. But the TL;DR is this: anyone can learn through a quality program, no matter the modality.
In my online classes, I am able to deliver more high quality lecture material than I do in my residential classes. Each video is tailor made in length for the topic covered and designed for typical learning spans, which don't cover 2 hour blocks. There are no digressions, sidetracks, questions from students that may not interest you, snow days, sick days, substitute professors because I'm on sabbatical, first year professors who are just getting their feet wet, and so on. We never get to the end of the semester and have to say, "Well, we're out of time so I won't be able to cover...". Just a pure form of the considered lectures of the best professors we have. You can watch speeded up, slowed down, or with subtitles, rewinding and fast forwarding, ideal for students for whom English is not their first language. For that reason I actually use some video lectures as part of my residential courses, since the in-person time is better spent doing other things.
In my residential sections, sometimes the digressions are the best part. The "war stories" of thirty years of pastoral ministry alongside teaching can be valuable. Sometimes students ask great questions, and the interaction is pure gold. We analyze texts from Hebrew translation to the point where we ask, "Now how would you preach Christ from that passage?" It is a fully interactive learning experience. Our students have lunch with me and the other professors from time to time; we meet and pray weekly. They build close relationships with one another.
On the other hand, our distance students spend 90 minutes with me every other week, so they get some of that. They don't have to break up the rich relationships they may already have in their home context. They continue to serve in their home churches, where they may be a youth pastor or ruling elder, without having to compete with twenty other seminary students at the best church near the seminary.
Our residential students have access to a great theological library. On the other hand, I have a distance student who lives in Princeton, with access to a far bigger one! And all the academic journals are now accessible online, along with a vast and growing number of ebooks. Course reading materials are almost all available online.
Our students are different: generally our residential students are younger, single or newly married, or with small kids; our online students are on average ten years older. That changes the educational experience too. A thirty five year old brings more life experience to the course; the questions he asks are different questions, less theoretical and more practical. On the other hand, a younger student may have the freedom to invest himself fully in the opportunities residential seminary life brings - bonding with other students and professors in friendships that will last a lifetime, playing ping pong and basketball with other students (don't tell their wives), and having a life-transforming time.
One of the things I noticed teaching residentially, before we had our online program, was that there were broadly two kinds of students: those with the freedom to pursue an optimum residential experience and those who were gritting their way through - working at UPS, as a part time youth worker, and raising a family, always on the edge of a crisis, who had no time to benefit from the residential perks. One of the reasons I noticed that was that in my own MDiv, I was both of those students: my first two years my wife worked and I studied. When we had our first child, she stayed home and I worked full time and studied full time. I read all the reading before class began, and did little other than study, work and spend time with my family.
Over the past year, I noticed that the latter group is now all online, even if they live locally. It just fits their lifestyle needs better; I would have loved to have had that option - indeed, I arranged some directed study courses that functioned in that way. But we have top students in both modalities. The requirements for the classes are broadly the same: the best students write just as good papers and other assignments. As Andrew noted, right now people who want to get into a PhD program should probably go residentially (though that may change over the years). But you won't necessarily get a "better" educational experience, just a "different" one. Which one is "better" for you depends on your life situation. Graduating debt free while retaining your sanity may make an online program look a lot better! And of course, not all online programs are created equal, any more than residential ones. Some online programs focus on churning through as many students as possible and are little more than diploma mills. But there are some pretty poor residential programs too. Do your due diligence to find out what the program you are considering is actually like. Talk to current students about their experiences. Or PM me if you want to know more about our program.