There has been a lot of talk over the hunting shotgun so id like to focus this post on the chainsaw, or least my feelings on it as I am not technical enough to have hard numbers from the files on hand but have a fair amount of hands on experience.
Prepare yourselves for a wall of text.
In its current form the chainsaw is indeed your "crowd" clearing weapon. By Which I mean your Katana, Claymore, Axe all do fine for clearing out single targets in sequence. The chainsaw excels in one area compared to the other weapons, its rate of Fire is phenomenal. If we assume that the wiki's information on DPS or otherwise is even halfway in the ballpark. you could say for every swing of the Katana, you could hit a target or multiple targets in a sweeping motion anywhere between 5-10 times in the span of a second or two at low damage.
This lets you cut down groups of Clots, Gorefasts, & Stalkers quickly by aiming at their heads. This also partly removes the need to have the proper timing to cut down a Crawler if you aim just right and leave your chainsaw out saving you a bit of ammo and allowing you to avoid swapping weapons and creating an opening if something blind sided you.
This in and of itself is nothing impressive compared to the damage the other Berserker weapons or the common sense to just pull out a gun and shoot crawlers before they get in range. but this is what gives the chainsaw its niche. You use the other weapons to kite and take enemies down one at a time acting like a mobile distraction platform for the team. With the chainsaw, you change into a gigantic wall. or preferably if you're holding in the right spot, "door" of death. You lock down a choke point and you rapidly cut through any weak Zeds that try to cross your threshold.
Realistically, this means you are sitting in one spot and just taking a beating from Husks unless you react appropriately. or are just letting Zeds get needlessly close to you when you could be more mobile and cut them down before they get to your group in the first place. This is all assuming of course that you are playing with your team as a sort of blocker and interceptor and not roaming around the map otherwise the chainsaw's choke point benefit and weight is counter productive. Suffice to say this is not the weapon to use if you're playing a higher difficulty aside from the well known strategy of spamming them against the patriarch.
So, with all this in mind, what would be a good time to use a chainsaw aside from the above mentioned trick? Quite simply, in maps with small
corridors or an obvious chokepoint not being watched by another squad mate, welded or otherwise. Biotics Lab, Bedlam, Inside Manor, Filths Cross, Hospital Horrors, Biohazard come to mind as possible candidates if your group so chose to hold down in an area with little movement room.
Alternately, you could use the chainsaw as a way to give you a quick killing clearing weapon if you were say, max leveled and playing with lower level, or lower difficulty friends and pubbies, and you felt generous enough to not show off your level 6 might to cut down every enemy in sight and waiting until they are actually "too close" to the group's perimiter to cut them down. Althoguh this is less a valid strategy and more compensating for having played the game too much without having to sit on your hands to enjoy a game with other folks.
All this in mind the Chainsaw should never be treated as a solo weapon, you should still have a gun and preferably another Berserker weapon paired with it when applicable to cover its very noticeable weaknesses. Axe/Claymore if you want Skrake stunning at the cost of a better ranged weapon. Katana if you want your speed while still having some weight left to buy a 44. for "quick" crawler clearing. Less effectively, you could just use your knife to close in and then swap to your chainsaw once in range if you do not wish to sacrifice the space, but this still leaves you open to Scrakes.
To those who read through this you get a gold star for listening to this long droning rant on things you probably already knew. To Those who didn't...
TLDR:
Chainsaw takes away the biggest advantage of the berserker which is speed. if you are going to use it, use it at a choke, try to have a medic to heal you, and make sure you have another weapon to switch off to to move quickly like a bullpup. overall its not as good as the other weapons but vs patriarch and clots its one of the best.
someguyhunter more or less summed it up already. : P