I don't have any comparisons with shetlands/minis. Actually, I have one. I had a small Shetland mare that was 37" at the withers. All 3 of her foals by the stallion below (45"), measured 37 - 37 1/2" at the withers. The one mare that I kept has been bred to a petite 40" stallion and we are expecting her 3rd foal from this cross. The first is actually smaller than the mare but built like her, the 2nd is now 2 and slightly taller but built more like her petite sire at the moment. As pairs, the first would drive with his dam and the 2nd with her sire.
BUT I have some with other ponies & full size horses.
Sired by our 45" shetland stallion - who himself was sired by a 45" stallion and out of a mare closer to 40".
we had 5 fillies out of a 48" Hackney pony mare. They varied slightly - with both the first mare and the last mare being the smallest @ 11.2 (1 +" taller than their sire... ) and the 3 in-between being the same height as their dam.
We had 5 siblings out of a 13.3 hh, horse-style mare. We didn't know her actual breeding but she had an awesome walk & sometimes was pacey. With her neck injury (s), we didn't regularly ride her - becoming less as she got older. All of her foals were very large at birth (scary!), slowing down a lot as they got older. The last colt was a sand eater and had to be euthanized @ 2 months of age - so we didn't see how he matured, The other 4 have/had been measured by their individual owners and all were right around 13 hh.
I was VERY excited to add the Arabs. I found the first mare - by accident! She was rather petite and small at `14.1. I was told that I'd get an "average" of about 13 hh ponies. Well, the 1st one arrived and once he figured out to get "growing" - he was taller/jwider than his dam when I sold him. At that time I was riding him and several times, I've regretted selling my ez keeper, 1/2 arab riding pony. Though the mare was small herself, she had much larger horses behind her in her pedigree and I thought that she would produce larger. Her purebred arabian foals have all been slightly taller than her, but not more robust. I didn't however, breed her again to see if my theory would be proven thru multiple breedings. The 2nd mare was larger, heavier framed/more substancial and also had larger horses behind her (at least in height - not sure in the bulk/substance area)... With two foals by the same stallion, she followed what everyone told me the Arab crosses would do - both her fillies stayed at about 13 hh but they were very wide and substancial. One sold as a weanling the other after she was a 3 yr old started under saddle and ground driving in harness. Both are ponies owned and ridden by adults - thought they are smaller than myself. The last Arab cross we did with this stallion was out of a smaller mare w/ some different breeding. She had no other foals and at this point probably won't have more (with us). Her colt by the same stallion is growing slowly - he turned 4 in Oct. He hasn't been officially started under saddle - however, he's been lounged some, had ground work and been saddled and "backed". Even had a 7 yr old boy tool around the round pen a couple of times. I haven't measured him recently, last measured 1 1/2 yrs ago at 12.1. I've been disappointed that he wasn't larger - but he's nicely framed (rather wide like his dam). He has grown, but don't know that he'll hit 13 hh. His dam is 13.3 & w/ my size, I spent a lot of time riding her for a couple of years. If he got as tall as her - he'd make a very fancy riding pony for an adult - right now, he's a decent size for a teenager that isn't too tall...
We had some other foals, would have to do another write up...
But my conclusion is that it really does vary and you just don't know and can get some serious surprises! Even with two ponies that I own that are full sisters - they are built different and move different. I had them measured with my stick at different heights but when I had them measured officially at a show last year - they both measured right at 40" - catching me by SURPRISE... I also feel that health, environment (care and training) and weather can affect some growth patterns... I have actually had more colts that didn't thrive or do well than fillies, but that's a whole 'nother discussion!