If you've yet to buy Exeter, just stick with Emmett. While there are certainly very good reasons to favor Exeter over Emmett (better accuracy and doesn't get chained to death by agility units), I'm not sure those reasons alone are enough to warrant investing the money into getting Exeter. In this case, the majority of the time your outcomes are essentially going to be the same (until you get to a point where you're very experienced, your losses will almost always come from your own mistakes rather than your unit having inferior accuracy, and even then, blunders are still a major cause of losses).

If you already have Exeter, I'd switch between both, depending on what the matchup calls for. For instance, I'd be more likely to use Exeter against a musket or swash, as Emmett's low agility makes him an easy target. Since he isn't a principal chaining unit, sacrificing being will based is a fine tradeoff.