It doesn't always reach capacity on NYE. It really depends on the whether. I have friends who arrived at the park last NYE about 3 or 4pm. There were no limitations on entering, but it had been raining all day. They said the park was pretty deserted and stayed that way all night.
When I've been on NYE, it has been packed, but I didn't try to leave and come back, so I don't know if it reached capacity or not.
Been several times on NY day and never had any problem leaving and coming back in the afternoon.
I guess it all comes down to what kind of experience you want. If you go on NYE, you do take the risk of not getting back in if you take a break. The evening festivities are a lot of fun. But how much would you really enjoy them if you spend the whole day in the park. You'd be exhausted. The safer choice is NY day, but you do miss out on some of the fun.