Rifle vs Pistol

Rifle

Increased ammo capacity, 66% more rounds per clip. Less frequent reloading and consumes fewer inventory slots, less Encumbrance and space on the Transport. In practice you can get through a mission with between 0 to 0.25 reloads per soldier. With Pistols you need at least 0.5 reloads per soldier, probably 1.0.
Option of much higher "shock" firepower at very close range (only), using Auto mode.
Weight not much more than a loaded Pistol, especially if equal amounts of ammo are carried.
VERY high (though slow!) Aimed accuracy. If have the time, and you need to make one shot count, this is the weapon you need.

Surprisingly expensive at $3,000 per weapon. Must be those laser sights...
Two handed weapon, impairs use of grenades and accessories.
Aimed mode has half the firepower of the Pistol's aimed mode, due to its slowness.
Auto mode is actually less effective than Snap fire (except at point blank range).

Firepower (effective damage dealt per turn) is basically the same or better than the Rifle vs light- to medium- armoured units (Sectoids and Floaters, even Snakemen and Mutons, if you dare). The exception to this is when the Rifle can be used on Auto at point blank range.
In fact, the Pistol is within 10-20% of the Rifle's killing power vs Sectoids, Floaters, Snakemen, Zombies and Celatids. (And about 2/3rds of the Rifle's power vs Mutons, Chryssalids, Ethereals and Reapers.)
In Aimed mode, Pistol firepower is more than twice as effective than the Rifle's (slower) Aimed mode.
One handed weapon, which gives flexibility with use of grenades, accessories, and scratch-use of second weapons (eg launchers).
Lower TU requirement gives greater opportunity for mobility, scouting while still preserving some deliberate fire and reaction fire capability.
Excellent for skill gain / training due to the high number of shots fired per turn.

Noticeably less effective than the Rifle vs medium-armoured targets (e.g. Mutons, Sectoid/Floater leaders).
Hassle in the Equip phase, as the game does not favour arming troops with pistol weapons and sometimes makes odd errors with them.
Ammo capacity limitations. Basically there is no weight advantage, since a Pistol + 24 rds weighs the same as a Rifle + 20 rds. In fact the Pistol uses up more inventory slots and Transport slots for the same "payload". Plus the Pistol is likely to need to be reloaded more often due to its faster fire rate (though the occasional Auto burst from the Rifle can even this up).