There's no perceivable difference between Sport and Sport+.

There is for me. Sport just has the touchy gas pedal. Sport+ you can feel more of the bumps and hug the roads better

Agreed, Sport has a more sensitive throttle input plus changes to transmission change logic, however the difference in damping ratio between Sport and Sport+ is imperceptible. I'm convinced steering is the same. Perhaps if you take it to the track you might notice the difference... not something I'm willing to do. I'm referring to an overseas version here, so ours might be a selection to nothingness whereas yours might actually work.

I notice a difference - steering feels more weighter and ride firmer, turns in a little better, feels more secure on the road. There's not a major change but I can feel the sporter nature.

Sport mode is a blessing for me in the 4RX (coming from a 2010 3RX). I use it whenever I need quick acceleration (having the need to cross multiple lanes in fairly short distance on a busy high speed express way from the far right to make a left turn). The 4RX turns into a 1000 lb lighter vehicle as the RPM can be increased quickly. I like the fact that the FSport has S and S+ mode as separate modes (explained by others already). Whenever I get nervous, due to driving at high speed close to impenetrable barriers or going thru super sharp turns, I switch to S+ and the steering feels more precise (probably with help from the suspension). If only quick acceleration is needed, the S mode is more comfy to switch to. The instrument display in the FSport is also more fun to have switching to these S modes.

Sport should be "normal". Eco is ok. Normal makes the transmission too indecisive.

I've been thinking about this post for the past couple of weeks and here are my conclusions, whether you want them or not, LOL.
1. Throttle feels the same
2. I could not tell the difference in the suspension unless I was going over speedbumps, pot holes, etc.
3.The steering is firmer, tighter and it's very easy to feel the difference.
4. Most importantly, and worth the price of admission, the above average roll of the RX when in a turn is reduced by 50% or so. I live in an area where there are many 40 to 50 mph sweeping turns and the difference while entering, during and exiting the turn is significant. I asked my wife if she could feel the difference as I alternated turns using sport then sport+ and she just said wow.
If you live in an area where turns are few, such as the south of Florida, the difference would be less noticeable.