Manual transmission BOXES last much longer than automatics. The clutches, however, vary with the driver. If the driver is good, then the manual is just as good as the automatic. If not, then the automatic's clutches will last longer.
This is true because there is at least one clutch for each gear in an automatic, and you can't replace them without rebuilding the entire transmission. You also can't normally operate the transmission if even one of them is unserviceable...they will cause the others to fail. Cost of rebuilding is $1000-$2500.
The manual has one large clutch. Replacing it requires temporarily removing the entire transmission. But good manual transmission drivers commonly have clutches that run over 100,000 miles (or even many hundreds of thousands). Cost of replacing a clutch is $450-$600. The clutch itself only costs $100-$150. The rest is labor.
The way to make an auto transmission last longer is to keep the fluid cooler. For most systems this involves a separate transmission cooler unit, possibly a cooling fan, and one of various types of transmission temperature sensor and gauge.
Yes. It is more expensive to maintain an automatic because it will eventually require fluid and filter changes which may not be within the capability of a Do-It-Yourself-er. The automatic will also be less fuel efficient in otherwise identical vehicles, by the very nature of the automatic's fluid coupling with the engine through the torque converter versus the manual transmission's physical coupling through the clutch.
You should note that Automatic transmission fluid change may not be required for the first 100K miles in some models. Materials in models that can be changed by a DIY-er usually cost $30-60 for fluid and about $20 for filter and gasket. For a shop to do it usually costs from $100-$300 (or even more) depending on the transmission.
But it is rare for an automatic to go much beyond 150K miles or so without a rebuild...because of the accumulated effects of heat on clutch material, soft parts, and normal wear on springs that most manuals don't have. The way to extend that time is by controlling transmission temperature.
So your friend is right, if we are talking about a driver who does not drive in a way that burns out clutches, and if he is going to keep the vehicle for a long time. Otherwise...it depends on how many clutches he burns out.
Or you might be right, if we are talking about stop-and-go traffic in an auto with a great transmission cooling system, or if you only intend to keep the vehicle for 30K or so miles as most people do.