You need to redesigned from Enemy Unknown‘s Sniper class, the Sharpshooter’s name change will reflects a more robust support for their secondary weapon, the pistol. Sharpshooters mainly focus on damage from a distance, either concentrated into powerful, single attacks with the sniper rifle, or just spread by out through a series of rapid pistol shots.
The Sniper tree supports the traditional role of a high damage dealer who then provides real cover for the rest of the squad from a distance. Ideally you then want to place all Snipers in one, elevated position that covers a wide swathe of the level. As a largely stationary position, it can be very tricky for Snipers to keep up with the rest of the squad and remain useful in timed missions that force you to keep moving. The Spider/Wraith Suit from the Proving Grounds can help with this, particularly with the ability to easily grapple up to high ground. Even if focusing on the powerful Sniper abilities at the top of the tree, quickly Return Fire and Lightning Hands that can add up to a lot of damage in the long run and allow for greater flexibility. Tracer Rounds, Scopes, and the Perception PCS all help mitigate the aim penalty from Squad sight. Auto-loaders, Repeaters, and Expanded Magazines can all help extend the chain of a Serial or Kill Zone attack.
Gunslingers, on the other hand, are much better at maintaining pressure while staying on the move, so you need to start reserving rifle shots for the more specialized situations. Lightning Hands, Quick draw, and also Fan Fire can easily stack to allow more damage done in a single turn than nearly any other class in the game. Experimental ammo from the Proving Grounds is most effective here, with their bonuses stacking for every shot. Dragon and Venom rounds are particularly good, immediately adding 1 damage in addition to sustained burning or poison damage. Armor, however, stings much more when applied to numerous, smaller hits, so be sure to come prepared with a Grenadier capable of clearing it first.
Please note that weapon upgrades will only apply to the sniper rifle, and it cannot be used for the pistol.