I can only go for a run first thing in the morning. Although, that's more about the empty stomach (and outdoor temperatures in summer). If I got sugar in my blood, food in my stomach, I kinda "crash" very soon and tend to get heart burn. The empty stomach also makes me feel lighter and the slight hunger feels in tune with the overall experience, if that makes sense. Running in the morning doesn't leave me tired, if I've reached the "maintenance level" (got no specific exercise goal, tho). Aerobic exercise has the benefit of giving me overall higher "energy" by making everything slightly less exhausting. And the peaceful calm of an early morning run in the green (city park) is a blissful, almost spiritual experience radiating into the day. That said, running in the evening can be fun, too, because I feel supernaturally fast. I do that too sometimes, if I feel very, very stressed/anxious and need an outlet.
On the other hand, doing strength training blood sugar is an asset, but pushing limits leaves me exhausted and tired no matter what. I presume, it's natural to feel tired, if the body has tissue damage to repair from exercise. The difference is, running can be done effectively (as far as health maintenance is concerned) without excessive tissue damage and inherently pushing limits as much.