TLDR - Switching jobs shouldn't make much (if any) difference to your H-1B visa interview.
The interview for an H-1B goes a little differently to that for a B-1/B-2 visa.
I know because I've done both.
The premise of a B-1/B-2 interview is that the interviewer is supposed to start off assuming that you intend to immigrate to USA illegally - and its your responsibility to convince them otherwise.
But since the H-1B is recognized as a 'dual intent' visa (in other words there's a path to permanent residency through an H-1B) you don't need to show strong ties 'back home' - in fact you barely need to show any ties at all.
My original H-1B interview a few years ago and the renewal last year were virtually non-events.
In the first interview I was asked a little about the company I would be working for and the work I'd be doing, but since the interviewer can't really be qualified in every one of the 100,000's of different professions you could be performing the questions aren't too deep.
For my renewal, since I had just changed to a different H-1B sponsor company, I was asked a little about the difference between the old job and new - but nothing unusual or particularly probing.
You do need to be prepared to answer these questions accurately and confidently though.
There are plenty of people and companies who try to scam the H-1B system to get into the USA illegally and you need to avoid giving this impression.
