Sparrows are mostly seed eaters, though they do eat bugs as well - typically NOT by catching them on the fly, however.
Soaring birds catching bugs on the wing are likely either swallows/martins, swifts, or goatsuckers (ie nighthawks, whip-poor-wills, chuck-wills-widows, etc.). The last group are mostly active at dusk and into the night; chimney swifts and swallows are more active in the day and evening.
if the birds have narrow, cigar-shaped bodies with long, thin pointed wings - they'll look something like a boomerang stuck on the body - then they're probably swifts. If the birds are a bit plumper, with slightly broader wings, and a tail that's spread much, then they're probably swallows.
By this point, martins are already massing into flocks to being southbound migration, but there are many other species of swallow that it could be.
Baton Rouge, Louisiana
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