First time doing this...
Note: I have never been on the Zephyr, and I haven't been on the Chief recently. However I have seen tons of reviews, video and articles.
First of all, they are both great, it really just depends what you want.
With the Chief: On the first day you get to enjoy sights of the Chicago suburbs and then Illinois farmland (Me, being in the the LA suburbs, I love looking at both of them.) The second day you wake up in the Colorado Plains, then enter New Mexico with the Raton Pass, which is a little part of the Rockies and a beautiful place. You then go through New Mexico and the great Southwest Desert, passing through Albuquerque. The next day you should wake up in Cajon Pass, or in the Los Angeles suburbs and then will be able to enjoy (if on time) some time in the Metropolitan Lounge before connecting to the Starlight. NOTE: IF you are late they will hold the Starlight for your train, they have done it before with the Sunset Limited and I'm sure they would do it for the Chief. Once you get on the Starlight you enjoy some Los Angeles suburbs, then for hours you enjoy the spectacular Pacific Ocean. Then you will cut inland and enjoy some California Farmland, which is lovely in it's own way. You will then pass through the bay area, possibly seeing San Jose, depending on when you go. You should wake up the next day in Northern California, and enjoy the beautiful scenery around Klamath Falls and then go straight through the amazing Cascade Mountains. Then through the Willamette Valley, which is honestly very pretty and a nice ride.
On the Zephyr, you will have basically the same views as the Chief on the first day. Then the next day you will wake up around or before Denver. You can enjoy some fresh air, and then breakfast in the diner. Then you will ascend into the middle of the Rocky Mountains. This part of the trip is spectatulalar, and unless you are literally 10+ hours late you won't miss it. You will enjoy mountain and canyon scenery for most of the day. When you awake, you should be somewhere around Reno, enjoying a bit of the Nevada Desert before going into the Sierra Nevadas, which is also very pretty. You then descend down directly into the suburbs of Sacramento. From here, you get what seems to be a not-very-appealing layover in Sacramento. On the Starlight, you should go straight to bed and then wake up in Northern California, same as the Chief.
Personally, I would go for the Chief/Starlight! You get plains, beautiful southwest desert, ocean, California farmland, Cascade mountains, and Willamette valley. It would make for a lovely vacation, and that layover in Sacramento just seems not good. As you would board the Starlight tired. When going the Chief route you also get to go straight through the middle of the street in Oakland on the Starlight, it's really neat!
Also, despite which route, I would suggest you go in the summer! Longer days, so more scenery. When you go in the summer you will be able to see more of Northern California. You will also be able to see San Jose, when travelling in the Fall and Winter, it's way past dark by the time you reach San Jose. And the ocean views are much better in the Summer.