It is a step up, and not a lateral move.
But the degree of how much of a step up it actually is from FSU to LSU is marginal. If there is an area that's more than marginal between the two schools, it would be with money...which is basically the same as fanbase.
LSU has much deeper pockets and can, and will, pay coaches and assistant coaches better than what FSU can do today. Right now FSU has to react to the market when it comes to what assistant coaches should be paid. Schools like Bama, LSU, and Texas can be proactive and set the market worth for assistant coaches. Schools like this raise the bar, and then FSU has to do a call blitz to all of our top donors asking for more cash. At some point one would think the calls will stopped being answered....or at least slower to pick up if not winning.
As an FSU fan, this is what scares me. Jimbo wants to win. And he knows in order to win he needs to be able to hire that best available coaches out there, just like he knows that we need to recruit the best available players out there. The difference with coaches and players, is the obvious. Good coaches are hard to find, and when you do get them, you better pay. We struggle with this.