Now, I'm no biologist but I would imagine DNA viruses are easier to vaccinate primarily because they have lower mutation rates than RNA viruses. However, even within RNA viruses, there's differences in mutation rates. Influenza mutates so fast (and is allowed to replicate out-of-control most of the time) to the point that vaccine escape happens within a year or so - that's why you need a new flu shot every year. As far as I'm aware, COVID-19 mutates slower than the flu, so vaccine escape will take longer.
Out of the three COVID-19 vaccines out there, two of them use an mRNA vaccine platform. This isn't because you need to match mRNA viruses with mRNA vaccines, but because it's just an extremely versatile platform to work with. In fact, for Moderna, stopping a worldwide pandemic was just a side project. Their actual goal was to produce custom cancer vaccines tailored to an individual patient's tumors. You can do this because the vaccine is just some genetic material and some nanoparticles to get it into cells. Your body itself makes the actual antigens that your immune system then fights.
So what will ultimately happen in the event of a vaccine escape is that Moderna and Pfizer will tweak their vaccines a little and the FDA will fast-track a new roll-out of the modified shot after Stage 1 testing. They already do this for flu vaccines - it's the only reason why we can even vaccinate against the flu in the first place. And as far as I'm aware, Moderna and Pfizer are both already trialling booster shots. Not so much because they expect a vaccine escape, but because they expect immunity to wane regardless of how fast the virus mutates.