"Deep Cycle" batteries, like marine batteries are made to be discharged 80%without sustaining damage. A deep cycle battery is designed to provide a steady amount of current over a long period of time. A deep cycle battery can provide a surge when needed, but nothing like the surge a car battery can. A deep cycle battery is also designed to be deeply discharged over and over again (something that would ruin a car battery very quickly). To accomplish this, a deep cycle battery uses thicker plates.
As a general rule, if you are going to use a true deep cycle battery also as a starting battery, it should be oversized about 20% compared to the existing or recommended starting battery group size to get the same cranking amps. That is about the same as replacing a group 24 with a group 31.
Again, while a Yellow top of equal size can last more than a few years, it will almost never last as long as a much cheaper non-deep cycle battery IF you are not draining the non-deep cycle battery down more than 10% or so on a regular basis. In your case, a 2-amp draw while the car is off is a fairly deep draw, so the Yellow Top may be a good choice.