I think it depends on your finances.
I would be happier knowing he just arrived in one piece safe and sound with no travel hassles if I could afford it. The trip cost would be for ME not necessarily for him.
He’ll have enough to deal with after arriving.
Two suitcases plus a backpack can be a lot on public transport when traveling by yourself.
Do these buses/trains even allow big luggage? In some cities, you are limited as to what can be brought onto a public bus.
I must be the only cheap skate in this crowd. No way would I pay $80 if there was a $6 option. I’m guessing the luggage has wheels and the backpack is on the back. I just spent a day with my adult kids, two of whom live in large city’s and my youngest who has been in NYC for one week. All three were fluent in public transportation options including, buses, subways, uber vs taxis and something else that I had never heard of. They were having a debate on the best and least expensive way to get to my son’s office in Manhattan. They finally settled on an uber something but when the bill showed up on my daughters phone, it was more than they had figured out. My husband reimbursed my daughter but - they each gave US money, because they felt bad about making the wrong choice! All three of my kids are super bargain hunters because of the way we raised them. I would give the OP’s son $20 and let him figure it out.
This may have to be looked up specific to each bus or train system.
Way too many variables and research! I’m just giving him the 80 bucks;)
Just sayin’…H and I went the cheap route once with just carry-on (so one small case apiece plus personal item)
Trip from hell. The trip involved not one but two elevators out of order. A TON of stairs. And a train that wasn’t running. And about 5000 disgruntled regulars. Our hour trip was closer to four.
Just tell him to keep a look out on the plane for a kid about his age with a teary-eyed mom giving the kid a lot of hugs and the dad looking stoic with hand on shoulder. It is likely parents taking their kid to the same school and maybe yr kid can hitch a ride. 
(Just kidding, sort of. I traveled by myself to Freshman move in and still haven’t gotten over how lonely it felt to see all those family groups helping their kid with move in. Maybe you could tell him that you can’t make it but you will spring for shuttle as yr virtual help.)
I would pay for the shuttle, for a freshman. I routinely paid for my son to take a cab back and forth ($25 bucks each way, including tip) when he didn’t have someone who could take him to airport. Now he’s 21, has navigated many trips on his own, and used transit systems in urban areas and internationally. This summer he took public transportation and shuttles in LA with 2 heavy suitcases and a big backpack.
I technically didn’t pay for D’s trips to the airport - it was to come out of her allowance - but because I’m a softie, I would conveniently slip her a $20 or so when she got home.
Whenever the kids went back to school, or if we visited, when we left we gave them what we call the “obligatory 20” (gave it to a cousin’s daughter too when we visited). Even though the kiddos are both comfortably employed and one is married, we still sometimes maintain the “obligatory 20” tradition.
**What’s missing from this scenario is WHAT AIRPORT and WHAT DESTINATION? ** Are we talking airport in some podunk metro area, or are we talking JFK on the other side of gridlicked NYC?
When my son uses JFK, its less stressful traffic-wise to take the train to NY Penn Station, then take the LIRR to Jamaica Station, then the Air Train to JFK.
OP also doesn’t specify whether it’s for arriving at school for the 1st tine, or for routine transit to the airport for breaks.
Recently I went to my grown daughter’s (and her BF) apartment for dinner. When it was time to go home, since I was by myself, D1’s BF got an Uber to take me home because they didn’t want me to take a public transportation. Pay back is nice. 
If the kid is paying out of the kid’s own money…let the kid choose.
Well, he does say it’s a male travelling with 2 suitcases and a backpack; no guy I know carries that much on break.
This may vary by individual, but there’s no way I’m schlepping 2 suitcases up and down the stairs at Penn Station, with the constant broken elevators and escalators, if I can avoid it. And for routine transit, I save money and take the “E” train over the LIRR.
jOD, were you ever really considering the $80 option? Sounds like you already knew what you wanted to do when you started the thread.
OP also hasn’t answered the question about whether this is the shared SuperShuttle option (where you don’t have to find ban pooled) or the solo option.
Lol, I was thinking the same thing…
H and I have caught public trains and transferred from airplane and then walked a bunch of blocks. We had a rolling carry on apiece AND a backpack plus another small wheeled bag. On the way back to the airport, we agreed to splurge on a taxi or shuttle instead. We found it exhausting wrangling the luggage and finding our way while sleep-deprived (after long red-eye flight) in a new city.
I would go for the shuttle. Two suitcases and a backpack on public transit would be a real pain, both for the student and others on the public transit. This is likely to be an infrequent trip so why make it more difficult than necessary if you can afford the difference in cost?
I agree with this 100%.
This is for Freshman move-in? Geez. I can’t imagine making one of my kids do it alone, let alone making it more difficult than necessary.
Whats also missing is whether OP’s son has traveled much before? Also does OP’s son currently live in a small town or a big city? Has the son been to the college a number of times already? Also no one has mentioned the fact the kid is moving in with only 2 suitcases…so I’m thinking maybe OP can’t afford the $80… I hope the kid is ok with his parents not moving him in.