H1b transfer denied, move to H4 and then file for H1 , or wait for new H1?

I have the option to come back to the country on an H4 and then have a company reapply for h1. Only used 3 years of my H1 so I have 3 more years.

How difficult is it to move from H4 to H1 as opposed to H1 to H1. Or is it nothing different. Can I file for H1 while on my H4?

If the company’s filing was denied, is it better to move to another company? Or have the same company refile with a new ‘specialized’ project