I think it really depends on
1) design of bullet
2) cartridge being used
3) expected range you will be shooting at
4) your preferred shot placement
5) and the type of deer. A big red stag weighing over 200kg live weight is very different to tiny little CWD weighing 30kg.
A monolithic kills by a combination of
a) the bullet expanding into a flower shaped saw rotating at high speed and cutting a direct wound channel through the carcass. In effect take a 1/2” to 1” diameter hole saw and cut a hole through the carcass. Death will be to the major arteries and nerves cut during this process. The bullet simply needs enough energy to take it through the animal.
At one extreme you have the likes of 8.6 Blackout shooting a 250 grain plus monolithic bullet at just below speed of sound, but with a very fast twist rate on 1 turn in 3” it stabilises with a very fast twist rate so it hits large amount of rotational energy, although actual kinetic energy from its velocity is very modest. Yet they have been used to take very large game such as bison and Elk.
At the other end I have used 243 80gn Fox launched at 3100 fps. And I have had these go straight through Roe and Red with no issues.
b) Temporary wound cavity - this is the shock wave created as the pushes fluids to one side as it goes through the animal. From spending a lot of time in boats over my life - a sleek long thin boat such as a rowing 8 produces very little wake (equivalent of an arrow). But bullets once they hit an animal actually become a square or blunt ended boat. A larger stubby will produce a big wake but with lower velocity, a smaller boat going faster will produce a sharper, faster and in many ways more destructive wake.
When I compare the 6mm 80gn Fox bullet out of my 243 with MV of 3100, against a 7mm 130gn Fox out of my 7x57 with a MV of 2800 I have noticed the following over tens of deer I have shot with both.
The 7x57 tends to punch a nice clean hole. Deer, both Roe and Red, are polaxed on the spot abd then kick for several moments. There is a 1” sized hole but then minimal carcass and meat damage.
With the 243, I have one or two run a wee bit before collapsing and kicking. There is a smaller hole, but a lot more bruising and blood shot meat around the bullet path and especially in the offside shoulder.
Which do I prefer - I think the 7x57, but the 243 is flatter shooting so more precise.
I have also shot several Roe with a little 51gn Copper bullet. Everything again has dropped on the spot. And judging by the way they penetrate I would happily shoot bigger deer if legal to do so.
The drop down in bullet weight and get velocity up probably stems from the need to have enough rotational spin to stabilize the bullet. So take the Fox bullets above - they are the same sort of lengths as the next bullet weights up - ie 80gn Fox is same sort of length as typical flat based 100gn lead core. If I used a pointed 100gn copper bullet in the 243 with standard 1 in 10” twist it probably wouldn’t stabilise.
I used to use 100gn RWS Softpoints in 243 and 140gn Softpoints in the 7x57 and 7x65R. I used to get quite a few running deer that would go 30 / 40 yards if not more. And on more than one occasion with the 243 the bullet blew up on the nearside shoulder with only minimal penetration into the vitals. Admittedly that was down to shot placement.
For the last six years I have been shooting copper bullets, and my experience is that they much better game takers than older cup and core, and given lack of fragmentation you can put them further forward thus taking out the nerves and major arteries in the chest cavity. The only downside of using the copper bullets is for the hound - she rarely gets a difficult to find shot deer.