I used to use a sim900 with a fairly small antenna although still big by contemporary standards. Now I am working with a sim7600 and the antenna that comes with it is positively gigantic. Below is a size comparison
Certainly doesn't look like it would fit on a contemporary iphone or samsung. Are there more reasonably sized drop in replacements or is this basically it and they have to be this big for some reason?
Google 1/4 wave vs full wave antenna
If properly designed, a longer antenna has significantly higher gain than a shorter one, for the same frequency.
Antenna design is a black art.
So it appears - both those illustrated are indeed - black! 
do you have any specific suggestions? All I can find are the giant style antennas on amazon and ebay. Only small dodgy sites seem to have one or two links to possible small antennas.
I disagree, but why is that size a problem for you?
An antenna that is not designed for the frequency bands in use, and does not match the impedance of the transceiver module will not work properly, or at all, and may even damage the module.
You have to know the actual frequencies you want the antenna for. I don't know 4g, but 5g is in the 3.5gHz range. When you know the frequency, you are in the first step to finding your antenna.
Don't believe a single thing they tell you about the antennas there. Most of the time, the frequency information is completely made up BS.
This is the module
it says the 4g bands are
LTE Cat-4 LTE-FDD: B2/B4/B12
I was just wondering does it have to be that size and type? I know that enduser tech is more advanced but if they can make tiny razor thin phones 4g/5g phones these days nobody's come up with a way to at least partially move in the same direction for diy tech and instead we're going the opposite direction with later more advanced devices needing much bigger antennas 4x the size?
Google quickly found the documentation for your question. 4G frequencies and antennas.
Enjoy.
I have a beginner question for you. I'm not a huge expert on antenna science. Are LTE antennas for other parts of the world compatible with each other? I found another more flexible antenna that goes along with this slightly different module on a different board sim7600ce-t vs sim7600A
vs
No. But if antennas are properly designed and matched to the transmitter or receiver, the longer one wins.
I'm not a huge expert on antenna science.
Very, very few people are.
Are LTE antennas for other parts of the world compatible with each other?
Yes, if they are properly designed for the frequency bands in use, and impedance matched to the transmitter or receiver. It is physics, which does not depend on your address.
Along with much of the rest.
They should be, but may not be. The problem began with the original cell phone allocations of 800MHz in US, 900 in EU. Then they went to dual band, so 800+1900 and 900+1800. Then they wanted phones to work globally. So many phones have quad band antennas, 800,900,1800,1900. It's not easy to do but they do it. But those are internal and it's possible to factory tune and calibrate them. So it depends what you call "an LTE antenna", when it's an external accessory that is not designed for a particular phone model.
To further complicate the picture: The local cell tower you are connecting to has a powerful transmitter and very directive antenna pointed your way. And your cell phone will increase it's transmitted power to it's antenna until it can properly be received by the cell tower receiver. The two do talk back and forth to each other.
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