Obligatory note: crashes are so incredibly rare on amusement rides, as are any significant injuries caused by a ride system itself rather than pre-existing medical conditions or poor judgment of a rider. So all of the below is a teeny tiny corner case, and should be thought of as such.
If a ride collision is an extremely light tap, and if passengers are seated, in proper position, and restraints engaged, then the odds of any noteworthy injury are very small. Very. If it's a significant hit instead, then there are a few things to think about: magnitude of the attendant G force (high), duration (very short), and direction (probably either straight forward or straight backward).
Since you suggested the case of similar initial train speeds between a train entering a brake run vs. a train experiencing a crash, the short answer is: the difference is very large between the two. And the easiest way to see this is to consider the amount of distance and therefore time the train takes to decelerate in each case: a couple dozen feet in the case of braking, and a very very small fraction of that distance in the case of a crash.
Some more detailed thoughts...
Braking is by definition a controlled deceleration over time. A detailed graph of speed vs. time will show a smooth decrease in speed with time, though the exact profile will not be a perfectly straight line. The slope of that line will show the deceleration at any point in time, and it is designed to conform to regulatory limits on how intense it can be. I may get the numbers wrong here, but I believe ASTM F2291 specifies a max allowable sustained straight-line deceleration of -1.5G for lap bars and -2.5 G for OTS restraints. For sufficiently padded OTS restraints there are more lenient limits (up to 2 seconds of -3.5G), but not for quick-onset braking situations. Anything above -2.5G has to be a more slow-onset deceleration, and really doesn't pertain to conventional sit-down rides. So it's probably safe to assume the max allowable "typical" quick-stop braking (e.g.) B&M aims for will correspond to an absolute max level of the bolded numbers above.
A collision is by definition an uncontrolled deceleration with at least one moment of very rapid deceleration; a graph of speed vs. time will show at least one moment of an abrupt "jump" up or down in speed, due to either hitting or being hit by some massive object with significant relative velocity. The graph likely will look like it has an impossibly steep slope for an incredibly small period of time, with accordingly high G force during that brief moment of impact. While a light tap may stay below 1.5G or 2.5G in magnitude, any really significant crash is likely to exceed that for perhaps a quarter-second.
So what's worse for something like soft tissue injury: 2.5G (or less!) of braking deceleration for a second and a half or 5-20G deceleration for a quarter-second? Likely the high-G, short-duration experience that involves a huge amount of energy transfer occurring in less than a split second. Human bodies don't like that sort of thing. Braking is a designed experience according to carefully crafted standards; the crash is a wild and way out-of-regulation phenomenon, and standards largely just say "don't ever do that."
Roller coaster trains sometimes feature visible bumpers on the lead and trailing cars, and the "squish" in these bumpers helps to draw out the distance (therefore time) over which energy is transferred in a theoretical crash. This can reduce peak G forces on trains and therefore passengers significantly, but unfortunately in a major crash they would buy only a foot or two of extra distance as they compress. So the train would still be experiencing a huge change in speed over a very short distance and therefore time. Mostly these bumpers prevent train damage during low-speed bumps, like station movement and transfers to/from maintenance. They are very partial mitigators of injury, rather than preventers of injury, in any theoretical medium or high speed collision.
Roller coaster trains don't have much in the way of designed-in crumple zones, except for those bumpers, as far as I know. Components may crush or bend in a crash, fasteners stretch, or train couplers buckle, absorbing energy and slightly spreading out its onset upon passengers. But there's only so much of that that can occur, and of course too much of it would mean Very Bad Things like seats no longer being attached to trains. That is fastidiously avoided when trains are (over-, OVER-) engineered.
All of which is why amusement ride vendors really do mean it when they talk about safety being their primary goal with every ride system. Collisions just can't be allowed to happen, and when they (very very) occasionally do it's a huge deal, typically with multiple system or (more often) human failures stacked up into a single situation.