Our youngest was 2 at the time of our last family trip to WDW and we did both of the activities you mentioned, without an issue at either, but then again we dined earlier at the CG...around 5:30-6:00. We select the earlier times since kids at this age start to break down from the long day they have already experienced...we watched the fireworks from other locations during our stay. CG is good and I would recommend the experience, but depending on the night service may move a little slower than desired.
I'm not to impressed with the diner show packages since the restaurants are exceptionally busy at these times taking away from the enjoyment of the meal. Also, depending on the time of year you are planning to attend you may not even need the dinner package to get a good seat. Most people do get there NLT 1 hour prior, so plan on bringing items to occupy your childrens time, which could also entail purchasing some items from the vendor who is selling night time lights and toys.
If you are choosing one of the two you mentioned, I would recommend the Fantasmic Show and Dinner.
You should be prepared with something to occupy the childs time as you wait for the show to start. Develop your own exit plan, since it will be an unknown how your child will react and you should not confine yourself to sit in the rear because of this unknown factor.
There are restrooms, food stands in the show area and before the show vendors will be selling light/glow in the dark toys. If this is also a late night for MGM and you plan on staying (if staying at a Disney Resort), just realize you will need to keep you stroller at another location and non-Disney guest may take your stroller after the show since they perceive everyone is leaving, which will leave you without a stroller if you rent a Disney stroller. People were stating Disney CM told them to take any stroller in an effort to keep the crowds moving as everyone was leaving the show area.