French press and pour over both use hot water and ground coffee. That's where the similarity ends. A French press produces heavy, oily, full-bodied coffee with sediment. A pour over produces clean, bright, lighter-bodied coffee with no grit. Neither is better. They're different drinks.
If you like the thick mouthfeel of diner coffee, you want a French press. If you like the clarity and brightness of what specialty coffee shops serve, you want a pour over.
French Press: Simple, Forgiving, Full-Bodied
Coarsely ground coffee sits in hot water for 4 minutes. Push the plunger down. Done. No technique required, no special pouring, no gooseneck kettle. A $25 Bodum Chambord is the standard and it's lasted people decades.
The metal mesh filter lets coffee oils and fine particles into the cup. This is what gives French press its signature body and richness. It also means sediment in the bottom of your mug. Some people love this, some hate it.
Cleanup is the only downside. The wet grounds in the bottom of the press are annoying to deal with. You can't pour them down the sink (clogs drains). Scoop into compost or trash.
Pour Over: More Technique, More Reward
Paper filter, controlled pour, 2:30-3:30 brew time. The filter traps oils and sediment, producing a clean cup where you taste individual flavor notes instead of a wall of richness. A light roast Ethiopian through a V60 will have fruit and floral notes you'd never taste in a French press.
The trade-off is technique. Water temperature, pour rate, grind size, and bloom timing all affect the result. There's a learning curve. First few cups might be sour or bitter while you dial it in. After a week of daily brewing, most people find their groove.
Equipment is cheap ($8-15 for a V60, $25-35 for a Kalita Wave) but a gooseneck kettle ($20-165 depending on how fancy) makes a real difference for pour control.
The Practical Decision
Morning person who wants coffee fast with minimal effort: French press. Grind, pour, wait 4 minutes, push. Done.
Someone who enjoys the ritual and wants to taste what they're paying for in specialty beans: Pour over. The 5-minute process becomes the morning routine you look forward to.
Making coffee for 3-4 people at once: French press. A 34oz press makes 4 cups. Pour over is mostly a single-cup method (Chemex handles 2-3 cups but takes longer).
Both are under $35 for the equipment. Buy both. Use the French press on rushed mornings, the pour over on weekends when you have 5 minutes to enjoy the process.