As I commented on your PRS Tremonti Review: The Super Les Paul Video, the two, whilst arguably are 'similar', they are also very different beasts. The 594 remit was to make a 'classic' 58 Les Paul because Paul would talk about 58 Les Pauls and none of his audience had ever played a 58 Les Paul, just the re-issues. Because of their price, their availability and rarity, its understandable that very very few people actually get to play a vintage Les Paul
The 594 was born out of that. From the 'Vintage' neck carve, the 58/15 LT's and of course the switch/pots arrangement - even the scale length is more accurate to the originals (I believe). Of course PRS add their own modern twist with locking tuners and the coil splitting - as well as the consistency and quality they are known for.
The Tremonti is, as you say, a hot-rodded Les Paul. Its remit is the requirements of Mark Tremonti, what he needs to make the type of music he plays. Its a lot more 'modern'. It has a Trem Bridge too - something that is not very 'Les Paul' and has a 25" scale length too. I believe it has the Pattern Thin neck as standard and of course the 'Tremonti' Pick-ups. I don't know exactly where the Temonti PU's fit, whether they are hotter than most or more vintage voiced. Its irrelevant in the whole scheme of things because the guitar itself is still a very different and much more 'modern' instrument in general compared to a more 'vintage' (classic maybe better because the instrument isn't old) 594.
I couldn't personally pick between the two. On the one hand you have a vintage/classic LP style guitar compared to a Musicians much more modern needs and PRS built signature guitar built loosely around a LP structure. Its like trying to pick between a Silver Sky and an Ibanez Jem - ones a 'classic' 63/64 strat type instrument and the other is a much more modern 24 fret 'super' strat built for a 'musician' specific needs - both have the same scale length and has some commonality but, like the 594 and Tremonti, you can easily make a case for owning both - one more of a classic built more of a 'general' instrument and the other much more of a modern musicians requirements, hence a 'signature' model.
I know the Silver Sky is a 'signature' model of sorts but its still designed to be a 'classic' Strat for all musicians that can't get a 63/4 Strat and John Mayer didn't want it to be a signature of sorts more of a collaboration with PRS to make a 'unicorn' guitar so that he, and everyone doesn't have to go looking for 'the one'. Both it and the 594 are 'classic' guitars with modern features (like locking tuners) and the quality and consistency that PRS have.
Because they are so different, with different remits, you can own both without feeling like they are too similar (other than the PRS quality) that you can only have one or the other. Of course if you prefer a more classic or more modern vibe, that can influence your decision on which to buy, keep and/or sell...