Aside from where the bar is in relation to ones chest, another huge factor in why a floor press is 'harder' and effective for building starting strength is that in a floor press you don't arch or use leg drive. In my experience a weight that I can floor press is relatively easy when done with the proper bench set up and leg drive. If my floor press improves, then my regular bench certainly does ( I can generally 3 rep what I can 1 rep on a FP). Give them a shot for a few weeks maybe as a main execrise and as a suplemental one. It's just more more tool in the arsenal. ( If your floor press is similar in poundage as your regular bench, I would evaluate your bench set up to see what you aren't doing correctly or as efficiently as possible. The floor press poundage should be less generally than your bench press, not always but generally speaking)
Another very beneficial lift to help raw benchers is the dead bench. Simply set a bar on the spot pins and press. Then return the bar to the pins, reset and press again. I tend to prefer hanging the bar from chains in my power rack so that the bar return to the exact starting point each rep. It helps me stay tight and properly set up. Plus, it teaches me to push straight up ro the bar will sway in the chains and I waste energy and can see that I'm wasting energy which is a positive reinforcement of proper form. Another benefit of the chain version is that I can adjust the height link by link vs the spacing on the spot pins.
Hope this helps.