Preference and advantage is pretty subjective. Depends on what your interests are. There are advantages to either side depending on what you're looking for.
The west side is the "quiet" side, around Grand Lake and further south, Grandby. Grand County is wide open beautiful, but it's a different kind of beauty. There's also fewer commercial campgrounds in the immediate Grand Lake area, but more USFS campgrounds around Lake Grandby. If you want to travel a bit, there's a wonderful YMCA campground (Snow Mountain Ranch) in the Fraser/Tabernash area, that is definitely worth considering, and that's on the west side.
There's also Timber Creek CG inside the park, and that is definitely quieter and less crowded. Unfortunately, the beetle kill of years past have taken a toll there and all the trees had to be cut down. It's still a viable alternative for dry camping.
The drive up the west side to the top, at the Fall River Visitor's Center, is not quite as dramatic as the drive up the east side, but it's beautiful nonetheless. And it's quicker to get to the top than from the east side.
The east side has Estes Park, and if you're looking for LOTS to do, there's a lot to see in Estes. It's a typical mountain tourist town, and it can get very busy, especially on weekends. There's more commercial campgrounds there, but they are also more expensive than on the west side. Right now, there's only 2 viable ways to get there -- US 34 from Loveland up the Big Thompson Canyon, or Hwys 119/72/7 (the Peak to Peak Highway), which is a beautiful drive, and would make more sense to take, given that you would be coming from Leadville. You could take I70 east to the Central City exit, and that takes you right to Hwy 119.
There's lots more to the east side as far as hiking and driving and places to see. The Old Fall River Rd will be closed this year, so that's not an option. But there are lots of alternatives. Bear Lake is a "must see", there are a lot of hiking trails there. It can, however, get very crowded on the weekends.
Whichever option you choose, it can be enjoyable! Also keep in mind that the sights on the east side can be visited from the west and vice versa. There's really no limit other than time as to what you can see and do on either side.
If you don't have an annual parks pass, it's worth consideration. Also, the day pass is good for 7 days in/out of the park.
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