I personally am a huge sandwich fan.
The spin-up time isn't as bad as it used to be and in my experience it is worth the extra damage the minigun grants you in pretty much all cases.
Some players like to use the shotgun to suppress enemies while on the move, but I think it is a better choice to use the G.R.U (to get there faster) or the Fists of Steel (to get there with more health).
A good example is an enemy sniper: While the shotgun might screw up his aim enough to keep you safe, in my experience being faster or stopping him from one-shooting you is more effective.
If your team does not have (enough) medics you need the sandwich pretty much. You are too slow to constantly run for health packs, plus your other teammates will do the same, often ending in races for the health pack. With the sandwich you don't need to run for healthpacks, you can heal fellow teammates if you don't need it yourself and you can convert small healthpacks into medium ones if you are at full health.
While you can just fight near healthpacks, that only works on certain maps and limits your flexibility quite a bit.
If you do have a medic that keeps you alive, it is always nice to return the favor with a sandwich, for example if you get flanked by a pyro and your poor medic is slowly burning to death. I also like to use it as a "healing booster": If you need to retreat from spam, walk around a corner, throw the sandwich on the ground and pick it up, allowing you to get back into the fight at full health within seconds.
Yes, if you have an over-abundance of medics - meaning you never have to heal your medic since they heal each other - the sandwich kind of turns into a waste of a weapons slot, but I very rarely have that problem.
Long story short: For my playstyle the sandwich is a much better choice, but I'd really recommend to just try both and see which one fits you more.