Yup.

More recoil and a slower barrel time resulting in more movement of the rifle before the bullet exits the muzzle.

I suspect that the 300 Gr. bullet is just shooting flatter. And the 425 Gr. is shooting higher because that is the correct Elevation for that Bullet weight and load as a Mid Range Trajectory. HTH Regards, FITZ. OLD TUCK.

Honestly, the only correct answer is “not enough information”.

It’s not likely a 10” difference do to any one factor, so you need to look at them all.

The most effect will likely be drop. Plugging both bullets and velocities into a ballistic calculator with a 5 yard zero and 0” above bore for sight height will answer that question pretty quick.

Bullet BC will be the biggest factor in drop. To say that the heavier bullet will “always have Less drop” is just flat out wrong. This can easily be proven by shooting the same bullet loaded forward and backward. The shot with the most pointy end forward will have less drop.

Kinetic energy/velocity drops very differently for different shape.

Recoil is again measurable, but I would argue recoil has less effect than recoil management by the shooter. Bracing for the heavier load will cause more point of impact shift than the actual recoil shift.

Shooting direction east to west or west to east will make measurable difference do to time of flight if you want to be critical.

Personally I always calculate the actual drop first, before I get into all the more subtle reasons. It takes most of the mystery out.

If anyone cares to, I've attached some actual data may cause some head scratching...   
A few details and description of data presented- Data is in the form of a PDF, targets are jpeg.
From the time stamp one can see there is less than an hour difference from one group to the next. 
I did shoot several other loads in the same period - total of 50 rounds shot.   This is not a small caliber (50-90 Sharps) - the rifle is a C-sharps 75- (32" barrel), comfortable, but not for wimps either...  The distance was 100 yards, off the bench, an economical Hoppes front rest with a small muzzle bag filled with rice.  Attached are pictures of these targets with correlating loads- not spectacular- but respectable.
My sight staff setting is noted in inches on my report, the 526 grain bullet sight setting is .590" and the 625 grain bullet sight setting is .620".  There are a couple other factors to note here- I forgot to change the bullet weight setting on the machine so kinetic energy calculations are not valid for the heavier bullet.  The load for both bullets was the same charge weight and powder- velocities do indicate this- had the powder charge been increased to same velocities would the sight setting been the same? would the group have been better or worse? If time and ambition permit I may go there in the future...
BC's are calculated from velocity averages using an online app - they indicate that the 625 grain bullet has a slightly better BC.  At further distances this proved to offer a slight advantage? - 600 yards the group held slightly under 2 minutes with the heavier and well over 2 minutes with the lighter (wind was moderate/similar in both) I don't have my sight settings for this distance right in front of me but I recall the setting for the lighter bullet being higher on the staff.
 
In summation, I'm not going to discount the theory that heavier recoil causes one to shoot high - that's more of an individual response.   I am going to agree with Dave regarding the kinetic energy theory - a body in motion...   I've also had some projectiles with severe weight differences but the shapes created a far different BC and this combined with the k-energy factor created far different down range sight settings (the heavy NASA bullet design in 38, 40, 44 and 45 caliber all come to mind). 
Best Regards,
Greg

GT wrote on Oct 20^th, 2019 at 1:44pm:

I think the theory is just fine myself, I was mostly wondering if the theory was being applied in a way that it fit the example. It just wasn't clear that velocities were equal when the two different bullets were fired.

In my revolver example, best I could tell shooting conditions were very similar, if not, identical. The bc of the bullet must have been similar, because it's the same bullet. The only difference is the velocity. The round that's about three hundred fps slower hits about eight to ten inches higher at 25yds with the same sight settings, for me. I was just thinking there might be other influences in addition to bc.

In an unrelated story, I was recently fiddling with a rifle that I'd like to use for coyotes after regular hunting season is over. I only use one load in it. My instincts are to let the rifle, sort of, free recoil to check how it groups. But, I like to watch the impact through the scope, so I grip the the forearm  down against the hunting rest I'll use in the field and it shoots noticably lower. All I figure, is somehow or another, I just have to be consistent.

All the reading I've amassed over the years points to Deadeye Bly's explanation being the correct one.