Imagine the dynamics when the contacts move. The magnetic field builds fairly quickly (within a ms or so -- depends on the L/R time constant, and how the coil is driven), applying a force to the armature (typically a steel plate in a relay). The plate pulls, dragging along with it the springs holding the contacts. The spring deflects some, due to the contact mass. At the same time, the contacts torque and bounce a little, depending on how much the spring flexes, how everything is centered, and all that. But that's okay because they're in flight between end stops. Fast forward 10ms or so, the contacts smash together; the plate and spring mass continue to move, the stopping wave propagates up and reflects back down them -- meanwhile the contacts twist and torque again from all this flex going on, but some ms later they may bounce up (entirely off the fixed contact -- contact bounce as such), and so on until the mechanical energy dissipates and the contacts return to a static resting position.
This all happens in a blink, so it's basically impossible to see by eye; it's visible on high speed camera, or with a scale model that's big enough (the delays are essentially proportional to the length scale -- which is to say, the materials have a fixed speed of sound). Also doesn't help that the movements may be microscopic -- if the contacts lift by mere nanometers, that's enough to measure electrically.
Conversely when power is released, the spring force takes over, and the contact swings slowly over to its initial position. The dynamic force is much less in this case; note that force increases as the armature closes on the coil, acceleration increases as it travels, so it really slams around in that case. (Which is also why holding current is many times lower than pull-in current.) The opposite isn't true here though. So it may happen that turn-off bounce is actually none.
But you can still imagine there might be cases, like if the contacts are fairly square/flat shaped, and that little amount of flex/rotation/torque that occurs due to the spring motion -- maybe that's enough to break the contact briefly. Or because the contact surfaces are rough (they always are), maybe the sliding motion that comes with the spring flexing, causes the contact to skip. Lots of possibilities.
Turn-off could actually be better under load. At high current, the contacts weld, microscopically; this will take some force to pull apart, not more than the spring force of course -- within nominal ratings anyway, or so we'd hope(!), but perhaps enough to hold the contacts together before snapping the little metal bridge, and then it's clear to the other side.
Or maybe not, because the sliding motion shears the weld point on its way out. Lots of possibilities.
In any case, yep, bounce is generally worse on "make" than "break", and not particularly great in general. If you can avoid making assumptions about either, you'll be better off. For example, a typical debounce circuit uses an SPDT switch and flip-flop, so that, on the first "make" after the switch is thrown in either direction, that state is registered at the output, and no amount of per-contact bounce will disturb it. (The contact would have to bounce completely to the other side -- a fairly absurd condition, or at least, we'd hope so..)
Tim