Delays are more often due to freight congestion than due to weather.
A connection from the City of New Orleans to a western LD train (such as the Zephyr) should be no problem. The City is pretty reliable, on-time wise, and lately, even when the train is late, it's not by more than an hour or two.
The Zephyr can be hit-or-miss. It's had some very bad luck these last couple of weeks, but some of that was due to equipment problems, freight train congestion, possibly even a freight train derailment mixed in there somewhere. Stuff like this you can't predict.
In the case of making the connection from the Zephyr to the Starlight, keep in mind that the trains run on the same track between Emeryville and Sacramento, in opposite directions. So, if you're running late, and won't be able to make the connection in EMY, hop off in Sacramento and that gives you a bit more time to make the connection. I would still book the connection for Emeryville, assuming you want to maximize your on-train time. Also, if you're not booking all of this in one itinerary and you are traveling by sleeper, be sure to have the reservation agent (by phone) make a notation on your itineraries that you are connecting from the Zephyr to the Starlight. That way, they'll know to look for you in Sacramento if you don't board in Emeryville (they can resell space if a passenger doesn't show, and the Starlight tends to be popular enough that sleepers could be sold out). If you're traveling in coach, it's no big deal.