There are several things that will help at Moody. Some of this is personal projection/wish fulfillment, but some of it isn't.
First, the Erwin Center is a true multi purpose arena, with the seats going back at a pretty low angle. Compared to dedicated basketball arenas, the farthest seats might as well be in a different zip code. Sitting in anything but the first few rows of the upper deck frankly sucks. Because of the bowl shape there's a plethora of really bad seating options in terms of angles even beyond how far away from the court they're located. The priority when it was built was creating a venue with a large seating capacity for various events, including registrations, graduations, concerts, etc.. Basketball wasn't exactly an afterthought, but it wasn't the priority it should have been, either.
Second, the location is not great. Okay, it's not on the other side of Austin, but the Moody Center being on the north side of MLK is helpful, IMO. Not a game changer, but helpful.
Third, the students became a low priority starting in the early 80s when growing revenue became THE driver for the athletic department. I've honestly never seen anyone campaign as hard or as successfully for the students to make a difference as Chris Beard has. Tom Penders did some of it when he got the job, and it helped. But Beard has way more clout than Penders ever did, and he's a better marketer/manipulator than Penders was, too. Having a brand new arena is a one time event that will allow a lot of changes for season ticket holders - changes that are going to make a lot of people very unhappy - that wouldn't have been politically feasible with the Erwin Center. It helps that CDC seems to see it much the same way, but Beard being the students' advocate for a much more impactful seating arrangement is critical, mostly because he's a very effective advocate.
There's also the matter of putting a successful product on the court, which I feel confident is going to happen. It would probably help if the team was more offensive oriented from a casual fan perspective, but winning trumps high scoring games.
It also probably helps some if the football program stays moribund, but I'd really really like that to change. Preferably in my lifetime, please.
So, to recap, the Moody is going to be a much better venue to watch a basketball game. The seating is much more dramatically vertical, so even the farthest seats aren't that far from the court. It's going to be much louder for the same reason. While distance wise it's not that much closer to campus than the Erwin Center, perception wise it is. The students are going to have a lot more premium seats in the Moody, instead of just behind both baskets (which at one point they didn't even have that). Chris Beard is going to be effective in making a difference with his continuous, energetic, eternally positive, and multi pronged marketing to the student body as well as to the general fan base. Lastly, as Texas puts a competitive, top 10/top 20 product on the court year after year, people are going to get excited to build a part of their identity around Texas basketball.
The idea Texas is going to equal KU in atmosphere isn't all that realistic, but Texas can certainly exceed United Supermarkets Arena while Beard was there.