I don't think any of the old effects look cheesy, including the 1933 King Kong. If you consider it cheesy, then your view of films is kinda jaded. CG looks cheesy. It'll never seem real. The effects in the original films were at some point real objects, be it miniatures or stop-motion creatures. It lends itself to making the film more real and less extravagant and over-the-top like today's films.

And for the record, the 1976 Kong OWNS. And I just watched the E.T. original theatrical version and I'm never watching the 20th Anniversary Edition again. Ever.