Having heard both the 580 and the R253, here is my subjective take on them (and I am human, and therefore subject to expectation biases, etc).
Both are very nice speakers and, I believe, unchallenged bargains when on sale. However, they are definitly not the same sound!
Music:
I would choose the Infinity for more delicate and detailed music such as an intimate jazz trio or classical quartet; it is a little lean in the bass area, but manages great detail of delicate nuances in the midrange and highs.
The JBL with the horn is the more dynamic speaker and it has more slam in general and adds more bass into the mix making it great for rock!
If you like to blast rock, no question, get the JBL, but after you add a sub, the infinity are very much fine as rock speakers, but not as good as the JBL (which is in its element).
Similarly, the JBL is not obviously wanting in detail, but the Infinity provides a bit more of a delicate touch.
HT:
For bigger sounds and effects, the JBL are the winner, but I believe the Infinity has the edge on speech clarity (especially if you get the RC263 center).
I suspect either speaker will be a welcome change for you. The JBL is definitely a good speaker for dialog, but the Infinity is exceptional (and the one you should get if speech intelligibility is of special concern).
If I was going to only have one system and listened to 50/50 music/HT, I would go with the JBL's.
The extra cost of the JBL's over the Infinity's does get you something (and should for 2X to 3X the cost).
If budget is a significant factor, don't forget that the JBL 580's often go on sale for $360/ea. as another option! Additionally, the R253's at ~$360/pr and the R162's at ~$180/pr give a great range of price points for some amazing speakers. Between these two series of speakers a buyer has a fantastic set of options without breaking the bank! It is a good time to be an audio lover!
I think the Infinities represent a better value, and the fact that they are not wholly dominated by the more expensive JBLs (in my mind) reinforces that. On the other hand, if you look at these at their original MSRP, you would indeed expect to start seeing some diminishing returns as the price increases, and that is only fair!
But as I said before, it could all be expectation bias!
Look at the JBL series, they have a raw beast/power type of look! I think
@Danzilla31 described them as having a "muscle car" look!
The Infinities have a comparatively refined/sophisticated (but vanilla) look about them!
