As someone who lived in two different Hillhead Halls of Residence but have friends who have stayed in most halls at the University (as well as private) I am happy to help answer any specific questions. Personally, living in Hillhead was amazing and it's great compared to private halls given that you meet and surround yourself with SO MANY more people than if you live in private halls, simply in terms of how many more people are around you.
If you have the funds, I would say that New Carnegie is by far the best halls to stay in. It has the most life going on in them, they are very social and spacious, which is great if you're a sociable person who wants to make a lot of friends. When I went into Uni, I picked Adam Smith, Fyfe and Wavell as my top choices as I just wanted it to be cheap, so I had more money to spend on travelling and so on. I soon realised this was the completely wrong choice for me so I asked to swap halls very soon after. It is so difficult to socialise in those buildings, as there is no actual living space, just a kitchen with a couple of chairs, no sofa or anything like that. I was so lost and upset as all my other friends in other buildings were super close to their flatmates and so on, but given that it's all just corridors down the hallway, open toilet cubicles and shower rooms, it's just a bit bad if you're wanting to speak to folk. Not to mention that all the doors to the rooms are shut and hard to prop open and actually hang out with folk in. You basically have to just all reconvene in someone's room to actually get ready together or pre-drink or whatnot.
New Carnegie was full, so I opted for Grant Court. Grant Court is great, super cheap and also relatively sociable. The main bonus of Grant Court is that the shower room is huuuuuge and there are two toilets in most blocks as far as I'm aware. The rooms are very small, but the fact that you have a living room area with sofas and stuff makes up for it.
Hillhead is also great given that they have SRAs on campus that can help you and provide support to students, which is great. The porters can also help you with broken lightbulbs etc. at any point of time. The fact that in comparison to staying in e.g. Liberty living or whatever is that in Hillhead you have about 10x the amount of people than in any private halls, which is great because you're always going to run into folk you know, pres are always happening somewhere etc.