My response from reddit:
Pfizer developed multiple candidates, not all of which were self-amplifying. The one that they have progressed the furthest in the clinic is not self-amplifying. The 2P modification does not just stabilize the spike antigen against transition to the postfusion state after contact with ACE2, it stabilizes it in prefusion form generally. The Spike without the 2P modification is unstable to multiple conditions besides ACE2 contact and is harder to express in cells. It's also worth noting that this modification is also in the spike antigen encoded by Pfizer's vaccine, and that it was not discovered by either of these companies but rather by Jason McLellan's lab in collaboration with the NIH.
Saying 'the good thing about the vaccine is there are no viral particles' doesn't really make sense. What's good about not having viral particles? Virus-like particles and inactivated virus are both vaccine forms that have viral particles which have well-demonstrated safety and efficacy and have been FDA-approved. In contrast, there are no FDA-approved mRNA vaccines and these vaccines have the disadvantage of containing other elements (ionizable and PEGylated lipids) which we might not necessarily want to generate an immune response against.
Saying it gets a better immune response than 'normal COVID' doesn't have much basis in fact and is probably wrong. In my opinion, natural infection is actually more likely to produce a 'better' immune response as it is more likely to produce antibodies and SARS-CoV-2-specific T cells in the upper respiratory tract and mucosa. This has the potential to result in 'sterilizing immunity', such that the virus cannot establish a foothold and replicate. You will notice that the definition of efficacy for the current vaccine candidates is preventing disease rather than preventing infection. This is because intramuscularly-administered vaccines are generally poor at inducing mucosal immunity, which is the kind of immunity needed to prevent infection by strengthening protection at your mucosal barriers. This is usually most effectively induced by natural infection or by intranasal vaccination.
EDITED TO ADD: Sterilizing immunity is desirable because preventing viral infection and replication prevents transmission. If all your vaccine does is prevent disease after infection, then you could conceivably still get infected and spread the virus/disease to others.
Epistemic status: Not an expert. Pretty confident I have it right. Incorporated feedback from commenters, and asking for more. List of edits at the end.
What the Moderna vaccine does is it contains a piece of code (RNA) which asks your body to create a protein that is very similar to the SARS-CoV-2 spike protein (which it uses to attach to your cells), but modified in such a way that it is more stable, and doesn't change shape. Otherwise, the easiest place for the antibody to identify and attach to the protein gets hidden by the rest of the structure. Your body then says, "Hey, that's something new! Let's attack it!" and tries out a bunch of different things.
A difference with the mRNA vaccines is that there are no viral particles. The only thing it contains are the code (plus other code that doesn't get used to generate things, but are useful in keeping the rest of the code stable). The amount of RNA you get in your two shots would be all that's needed, and your body doesn't make extra strands of RNA that would ask for more spike proteins. In other words, you only get a protein that exists on the shell of the SARS-CoV-2 virus, and not there virus itself, so there is zero risk of infection.
Side effects are minimal. Less than 2% of the people get a fever, and most don't even have a headache. Just some muscle pain etc near the injection site. However, according to a commenter (see precog's comment below), there are some disadvantages, including the possibility that, while it might prevent disease, it might not prevent infection and transmission. Also, the lipids that hold the RNA might generate an immune response as well.
The Pfizer/BioNTech vaccine works slightly differently, but it's a similar idea. Have RNA code to produce the antigen to get an antibody response. It uses the same stabilization modification, which was discovered by Jason McLellan's lab in collaboration with the NIH.
These two are the first ever mRNA vaccines. mRNA vaccines are very modular, as well as easy to change and modify; most labs would be able to make their own vaccines with machines they already have. I've been following Moderna for a few years, and they were working on a MERS vaccine in the past. 4 days after the SARS-COV-2 genome was uploaded, they'd decided which sections they want to use, and which edits needed to be made, and they started manufacturing it (not mass production) literally the next day, and that was still in January.
edits: Incorporated information from precog (see his comment). Removed the self-propagating claim. Added a bit more information about Pfizer's vaccine. Changed wording regarding viral particles. Removed mention of a better immune response. Added disadvantages. Added clarification that there is zero risk of infection. Temporarily added a link to the Guild of the ROSE.