In my opinion, Unarmored Defense: STR+CON* would be slightly stronger than Mage Armor, but not unbalanced.
*(while not using shields or armor)
Unarmored Defense in general is relatively weak compared to mundane armor proficiencies. For example, say a character starts with a 16 in both Unarmored Defense attributes. That gives them 16 AC - the best starting AC possible. Compared to other armors:
- Mage Armor & 16 DEX: 16 AC
- Light Studded Leather & 16 DEX: 15 AC
- Medium Scale Mail & 14 DEX: 16 AC
- Heavy Chain Mail: 16 AC
So at level one, unarmored defense is, in the best case, equal AC to most other armor proficiencies.
However, Unarmored Defense falls behind later on. Medium and Heavy armor users can purchase armor upgrades with gold, while Unarmored Defense users must spend their ability score increases to keep up. Furthermore, if this Unarmored Defense is patterned on the Monk's ability, it prevents the use of a shield, putting it another 2 points behind for those classes who can use shields.
The presence of Magic Armor puts Unarmored Defense even further behind, because magic items which boost unarmored AC require attunement, while basic magic armor does not. Furthermore, Unarmored Defense requires that the player spend all their ASIs to keep their AC up, preventing them from taking Feats.
The specific ability scores tied to Unarmored Defense make a difference. Weapons which use Strength exclusively tend to be more powerful than Finesse weapons, so having Strength in Unarmored Defense will give the character a slight damage bonus. Also important to consider is how many ability scores the class as a whole will need. A Barbarian, for example, requires three ability scores: Strength, Dexterity, and Constitution. The Barbarian, however, can use a Shield.
By level 20, a character can reach 10 + 5 + 5 = 20 AC if they spend four out of five ASIs to improve their Unarmored Defense attributes. At that point their AC is equal to Full Plate + Shield. So while Unarmored Defense may produce somewhat high AC, it requires a huge investment, and precludes the use of many feats.
One of the clearest comparisons is to Mage Armor: 13 + DEX. Since a character using Unarmored Defense: STR + CON will probably start with a +3 ability mod from CON, and then not increase CON until level 16, when they've reached 20 Strength, the two features are almost equivalent for most of the game. Almost, because Strength allows the character to use stronger weapons than Dexterity.
So in conclusion, if you can account for the stronger weapons that become available due to tying AC to Strength, then yes the feature is balanced. Or maybe you're a DM that gives out magic armor, in which case Unarmored Defense is underpowered. Either way I don't see any way that this feature could be exploited for something all that much more powerful than what an ordinary character could achieve.