your experiences may differ from mine, but heres my take after 50 years of mostly ELK and mule deer hunts.
if you've been consistently successful using your current rifle theres no reason to change.
the most common problem I see is not the rifle or cartridge, used its the operators inability to accurately place shots under field conditions.
accurate shot placement is by far the most critical factor, if recoil effects your accuracy , go with the cartridge your more comfortable using.
one of the more successful members of my hunt club has used a 270 win for decades,many guys stick with a 30/06
I'm in full agreement that the 257 roberts,25/06-6.5mm- and 270 win and even the 308 win class of cartridge
throwing a 100-165 grain bullet in the 2600fps-3200fps velocity range is about ideal for most deer hunting ,
I've consistently had excellent results with cartridges in that class on deer
(the 25/06 , 257 wby and 270 win are personal favorite's)
yes these have also worked on elk. (seen it done many times)
but as your sure too be aware ,as is anyone who has much experience,
shot placement is very critical,hit correctly almost any center-fire cartridge can work reasonably well.
even with very good shot placement, in my past experience, about 40% of the elk run after being hit
yeah, I,ve often wondered if elk being a reasonably large,400-800 plus lb animal had a tendency,
if wounded,,too stomp and gore hunters like a cape buffalo ,or claw and bite like a Kodiak bear,
if we would see what I consider rather un-realistically light caliber rifles being used on elk.
I know a few guys in my hunt club think theres nothing unsporting or unethical in using a 24-25 caliber rifle,
on elk, I know of a few cases where several follow -up shots were required,
now obviously bullet selection shot placement and hunter skill plays a huge part here, not just the cartridge used....
but still I think if the hunter could reasonably be expected to be at serious risk if he failed to deliver a first shot stop mortal wound,
we might see a shift to larger bores and a bit more power in respect to the consequences of failing to deliver a rapidly lethal wound
anyone using those rifles needs to wait for the correct shot angle,
and be well within a reasonable range to consistently destroy the vitals,
get that correct and "your golden" in most cases, deer are as you stated far more "fragile",
and not as heavily muscled , a fast expanding projectile in the upper heart/lung area does impressive damage.
a bullet designed for elk generally zips through, and while its frequently going to cause lethal damage , its slower expansion,
has occasionally resulted a a tracking job for the rather short distance they run until they bleed out.
heart lung lower center chest
upper chest spine/shoulder
elk are a bit more heavily built , you benefit from deeper penetration, and a bit deeper penetration, is beneficial.
the same deer cartridges can work, on broadside shots,but a larger caliber you bring a bit better tool to the job,
if you select something like a 165-250 grain bullet in the 2300fps-3100fps velocity range,
are about ideal for most elk hunting, (in my experience) these cartridge's tend too consistently exit on chest shots, after taking out the vitals,
even if a foot or two of non-vital hide and muscle on a raking angle protects the vitals.
shots easily and ethically made with the 30-375 calibers but best avoided or almost mandating a premium bullet, with the 24-25 calibers,
and requiring a premium bullet in the 26-28 calibers in some cases
in 45 plus years of dressing out game Id suggest a 270 win,308 win, or 7mm 08 loaded with a premium bullet is about the smallest calibers,
I see consistently and quickly put down game effectively
yes a cartridge like a 257 roberts or 6mm rem, or 243 win in skilled hands works under nearer, ideal conditions
but if that elk of a lifetimes standing out at 300 yards and I need to make a less than ideal shot angle shot,
Id rather have a higher quality 180-200 grain bullet in a 30/06 or a 225-250 grain in a 338 caliber