True, but it's a little more detailed than that.
Armor essentially provides you with the same benefit of scale mail (AC 6) but without the weight or the casting restrictions. It stacks with Dex (and with a shield if you happen to have another class that allows shields). If you are wearing better armor than the spell provides, you gain no benefit. That also includes robes, etc, I believe, although it does not apply to Dex benefits or rings of protection.
Shield gives you an AC of 4. Additionally, your AC drops to 2 against missiles. Both effects stack with the Dex bonus to AC and rings etc. If your AC is better than that, the Shield spell does not override it. Potentially the largest benefit to Shield is that it utterly blocks Magic Missile and Mordenkainen's Force Missiles, including the small area of effect blast of MFM.
Both are good. Armor, because of the longer duration, is excellent for providing your beginner mage with a half-decent AC in the early going. It's good bang for your buck in terms of helping to keep your mage alive in successive close-quarters fights. Shield is a better all-round spell except for the duration.
The biggest difference is that Armor is sort of a generic, long-lasting protective spell, while Shield is better used as a single-fight spell, especially against anything that casts MM (Imbued Wights, Stone Nuisances, most NPC arcane spellcasters).
If you're going to cast Armor, cast it as soon as you wake up from resting (or as soon as you get into the area you are fighting in, if you have to travel). Cast Shield as a buff-spell-before-a-big-fight or against certain enemies.
I overwhelmingly prefer to have my mage hang around the back of the party to avoid being targeted. In many fights, neither one of these spells is needed.