I've stayed at both Burton & Garran Hall (B&G) as well as UniLodge (the group of Kinloch, Lena Karmel, Davey & Warrumbul). I think it depends on what kind you'd be after. UniLodge is self-contained apartments, ranging from single studios all the way up to 6-person shares. B&G, like Fenner and Wamburun - you have your own bedroom but you share bathrooms with people on your floor, as well as the kitchen with the whole college. Obviously the downside is having to share, and leaving your room if you need to use the bathroom or kitchen, but there is also an upside as the kitchen is a great avenue for socialising and meeting people.
Burton and Garran
I might be biased, but if you're deciding between B&G, Fenner and Wamburun - I'd pick B&G. Firstly, the B&G kitchen is massive and we each have our own dedicated fridge baskets (lockable) and kitchen appliance storage areas (lockable), as well as freezer sections (if we want to). We each have a designated spot basically to keep our stuff and a designated cooking bay, but we are allowed to leave it and use another bay if we want to cook with our friends. The kitchen can hold literally about 500 people. It often gets busy at dinnertimes (you will definitely have room though, just no peace & quiet) - so if you want somewhere quiet you might consider UniLodge. However, B&G is a very old building (many decades old), and there are no lifts so it is annoying if you have a room on the 3rd floor. B&G's rooms are also the smallest, but you do have free laundry (one of the only few colleges to do so I believe).
Wamburun/Fenner
I haven't visited Wamburun, but from what I've heard students do not have a designated area in the kitchen to keep their stuff (like pots/pans/cutlery etc.). However, the thing about Wamburun is that it is a very new building. Also, the rooms are larger than at B&G - students get double beds as well as a mini fridge in their room (you don't get a fridge at B&G but you can definitely buy a small one yourself to go under your desk). Fenner's kitchen is quite tiny, so you can't really fit a lot of people in there, and often you may have to keep your stuff with other people (I don't think you have allocated spaces like at B&G - I really can't remember but I did visit Fenner cos my friend lived there but I didn't seem to like it). Fenner is also a very new building, but they have had recent problems with their fire alarms constantly going off for no reason.
B&G is also cheaper than both Fenner & Wamburun, which kind of makes sense as it is very old, but you also get a great kitchen at B&G too. Fenner is very well located, in the middle of campus basically so easy access to many classrooms, the takeout places as well as the city. Meanwhile B&G and Wamburun are next to each other but it is a bit of a trek if you want to go to the city. In terms of culture, again I might be biased but B&G has a very long, established culture. Wamburun only came around in 2019 so they are very new, whilst Fenner has also been around for ages, but used to be off-campus so the culture has changed a lot since moving on-campus. If you're really into arts though, I'd say Fenner is pretty good for that, while B&G has great engagement in sports.
UniLodge
Obviously being self-contained apartments and relatively new buildings, the facilities are not bad. One downside is that you may have to clean everything yourself, whereas at the other residences the communal facilities are cleaned by cleaners. However, you may prefer to clean your own mess anyway

. A lot of people have said that there is no 'social life' at UniLodge because everyone is stuck in their rooms but I don't really think so - it is up to students themselves to be involved. You could stay in your room the whole time, or 'force' yourself to meet people at events. The thing is, UniLodge's resident's committee have a *huge* budget and can afford *tonnes* of free food-related events. UniLodge is arguably the best located, it's only a 10min walk (like <1km) to the city.
At UniLodge, I lived in a single studio so I can't really speak to the experience of sharing or having bad housemates. However, you do have your own bedrooms within the apartment - just sharing the kitchen and bathroom and the larger apartments have a nice living room too. UniLodge's walls are also very soundproof unlike B&G. However, some people have had issue with UniLodge administration. As UniLodge is privately-owned (while B&G and Fenner are ANU-owned), they do charge quite a bit of high fees for things and will often try and find ways to charge you more (e.g. for cleaners to clean your room if you fail inspection). UniLodge also does not have free laundry ($3 per wash/dry). I also believe UniLodge owns Wamburun so I'm not too sure how Wamburun admin is run, but Wamburun does have their own residents committee separate to UniLodge!
I would definitely decide between UniLodge or B&G. B&G is also the cheapest too. But it depends I guess on what kind of kitchen/room setting you'd like and if you don't mind the location.