Export/Convert mov to mp4 output file bigger and bad quality

Hello!

In former times I used to make videos with premiere.

Nowadays I thought about buying premiere again and tried out premiere elements (to check out whether this cheaper version is good enough for me). But I was pretty shocked by the low quality of an exported mp4-file. Input was an about 80 Mb size-mov-file. The output mp4-file was bigger, about 90 Mb, and had unacceptable bad quality! 

So I change to an only-converting-programm "Free mp4-converter" (premium version (30 Euros), for windows), the result was a pretty good - small file about 17 Mb and GOOD quality.

Did I something wrong or ins't possible to get good results with premiere (elements) for converting mov to mp4?