First pay attention to the notes which are common or held between chord...
...ideally you don't want to change fingers on those tones unless a change of position is necessary. So, instead of thinking it's three finger placements in the first chord followed by four finger placements in the second chord, think of the first chord as three fingers placed and then finger
3 splits to fingers
4, and those movements are only by step so the fingers simple strike the adjacent keys.
...slightly different chords (often differing just by one key)
If those small movements of shifting the fingers around by step is difficult, I think you might want to spend some time on 5-finger, independence drills. It seems like your fingers may not all be equally coordinated. It should be easy to find many method books with 5-finger drills.
A related exercise you could try is something like this...
...I made the example with the inner fingers playing short values while the outer notes are held, but you can shift the short value quarter notes around to the voices of the chord so that each finger gets a turn playing with the quarter notes.
Don't overdo that kind of exercise. It may bother your hand. The point is to train each finger to move without the other fingers moving uncontrollably. You can also find a lot of things like this in method books.
Finally, I think a great way to train the hands to automatically hit the chord changes is to play the change and then repeat at various octaves...
...I've practices like that using a "gravity drop" movement where you lift you hands fully off the keyboard (which of course you will need to do to move a full octave) and then let your hands fall onto the keys with just the force of gravity.
Part of the point of gravity drop is economy of movement. Let gravity provide the power into the keys. But to do it right you must hold the hand and wrist with some firmness so the momentum moves through your arms, wrist, and hands. The benefit for block chords is you must get your hand into the correct fingering position before you drop it onto the keyboard. The challenge is to "lock into" the chord position with a lot more spatial sense when you aren't even in contact with the keyboard. Also, a fair amount of "visualizing" when you intend to drop your hands helps.
...much trickier than broken chords, as they require placing multiple fingers on respective correct keys all at once
To some degree you can think of many piano fingerings and basic musical elements as both simultaneous and broken notes. While not about your specific question regarding chords, this method books teaches scales as simultaneous finger groups which then are played disjunctly for scales.
...that image is a bit of cut & pasting from Knott, Scale and Arpeggio Manual.
Again, that isn't directly about your chord question, but you noticed the difference in playing chord notes broken versus simultaneously. Perhaps if you think about scale as both blocks of notes and disjunct, it might help you get the feel for playing chords as both simultanous notes and broken... as simply different rhythmic articulations of the same fingerings!