Both versions cover the same core experience — horseback ride, the Seven Bulls rock formation, the waterfall walk — the difference is what happens after.
The day trip gets you back to your Karakol hotel by evening, which suits travelers on a tight schedule or those who'd rather sleep in a real bed. The overnight adds a night in a yurt camp deeper in the valley: dinner with a host family, a genuinely quiet evening away from town, and a slower second morning before heading back.
If this is your only stop in the region, the overnight version gets you more of what people actually remember about a Kyrgyzstan trip. If Jeti-Oguz is one stop among several on a tighter itinerary, the day trip does the job without eating into time you need elsewhere.
Zoomy