I made the same switch a while back but eventually I moved back to Gillette.
What I learned was:
There are a bunch of things involved in a decent wet shave, the razor is only one part of it.
Preparation is key - exfoliate every week and moisturise daily, warm your face before shaving (lots of hot water), ideally shave first thing in the morning (your face muscles are more relaxed) and apply shaving foam gel with a brush (it works it in and softens the bristles better).
Razor burn is as much caused by technique as tools - shave downwards, all over the face once. Ignore the fact it still feels stubbly, you're taking off the worst of it. Now lather up again (avoid a razor on bare skin, that's going to burn) and do it again. Finally one last time (having lathered up again) going up the face if you have to to clear up anything remaining.
Then cold water to rinse, and moisturise afterwards.
On top of this an old fashioned safety razor did make a positive difference both to how clean the shave was and the razor burn (remarkable given that it's one fixed blade) but for me the extra effort involved in shaving with an old safety razor wasn't quite worth it. I like to be able to be a bit careless first thing in the morning while I'm half asleep and I can do that with a Gillette Fusion.
(Can I just say, for the love of god anyone making the move read up on how to shave with one first - it's not the same and you will cut yourself to pieces if you go at it the way you go at it with a modern Gillette).