It's the difference between holding up a weight by by hanging it from a cable vs. putting it on top of a column.
A tank that starts out round (ideally, if it starts out spherical) and is pressurized will tend to have its shape held by the pressure of the material inside. Basically, the internal pressure will try to make the tank round, so if that's the starting point, the internal pressure will, to some extent, help support the tank.
Think of a balloon -- the walls essentially don't have any bending strength, yet the balloon can hold pressure.
A tank that's maintaining a vacuum has an unstable shape: it wants to suck down to nothing. A perfectly spherical tank can withstand that, but it's not stable in buckling. Any dent will tend to "want" to get bigger; this tendency will have to be opposed by walls that resist local bending even as they're getting compressed by the outside forces.
And yes, if you were going to sink a tank in the ocean, and if it otherwise made sense to do so, starting with it pressurized before sinking it would be a good idea. Another sensible idea, if it fits what you're doing otherwise, would be to leave it open to the seawater and just let it fill as it sinks, then purge it once it's been installed.