What use is the shotgun for the heavy?

Spy checking while moving. As I run from the back to the front (when an engineer hasn't built a tele) I use my shotty to spy check the usual spots, without slowing me down.

As Powerlord points out, it's also useful when you inevitably run out of ammo.

You need a shotgun when you can't use you primary weapon because it's either slow or slows you down. This can happen in several situations:

• If you suddenly engage in a close-range fight. If you start spinning your gun, it's possible you'll be dead very soon.
• If you need to get somewhere fast and you still need to shoot on the way.
• To use a crit from K.G.B.
• If your main gun is out of ammo. That also happens.

The sandvich is a great thing, but it won't help you when you are out of ammo or if you need to fight in tight spots. I usually run with the sandvich, but I can't deny that shotgun is very helpful in some cases.

Like many TF2 items, the Sandvich is a sidegrade as opposed to a clear upgrade or downgrade.

As @TheAnnoyingPyro pointed out, I already talked briefly about the Sandvich in relation to standard Heavy builds.

The Shotgun has one major advantage over the minigun family: It has no spinup time. The Tomislav negates this disadvantage some, but not completely.

The important thing to remember is that the Sandvich has two uses:

1. To heal yourself for 300hp by eating it
2. Throwing it to heal a teammate

As tempting as it is to use it on yourself, if you have a Medic, you should save the sandvich to throw to the Medic if their health gets low. You can also throw it to a teammate to heal them (and put them out if they're on fire), then pick up any medkit to get another.

The Sandvich has been updated so that throwing and picking up your own Sandvich will no longer heal you... instead it simply replenishes your Sandvich ammo. It still heals allies for half their health, which is invaluable for a Medic buddy.

However, this isn't just between the Sandvich and the Shotgun... it's between all the Heavy secondaries.

• The Family Business gets 8 shots instead of 6 before reloading, at the expense of doing less damage per shot. While that may not sound useful, if you're on a crits-enabled server, it means you get more chances of doing crits before reloading.
• The Dalokohs Bar/Fishcake increases your health by 50 for 30 seconds (or heals you by 100) when you eat it. Ignoring stat changes, this means you have 350 health instead of 300. The downside is that it heals you much slower than the Sandvich (which heals you by 300). It takes 10 seconds to recharge, or like other sandwiches, can be recharged instantly by picking up a health pickup while at full health.
• The Buffalo Steak Sandvich temporarily locks you to melee only, increases your speed, and makes all damage you deal and take Mini-crits. While this may not sound useful, it pairs well with the KGB and Holiday Punch. Did I mention the movement speed with the Steak Sandvich effect is the same speed as a Medic? The Steak Sandvich can also be thrown to allies to heal half their health, just like the Sandvich can.
• The Panic Attack gives you 6 shots before reloading and has 50% faster deploy time + 50% more pellets per shot. However, it has a wider fixed shot pattern, does 30% less damage, and successive shots (eg holding down primary fire) increases the width of shot pattern: it becomes less accurate if you continuously fire it. Note that the shot pattern resets if you stop firing or reload.