Well, do you want to compare stock for stock or highly modded to highly modded? There is a lot to compare here.
Potential wise you cannot make the same power with the LS1 as compared to a mod motor all things being equal. Put simply, when optimized for what ever particular combination they are running multiple valves make the difference in this comparo as they have in most comparos for decades now. Strength of motors also plays a part.
There are 4.6L DOHC mod motors with what is basically a stock bottom end making 1500hp with twin turbos. (Improved bearings and oiling being the only mods) A stock block LS1 is incapable of making that kind of power reliably even at 5.7L/350ci. Even with forged internals the block just cannot do it. (To be fair the old Windsor Ford blocks cannot take much more than about 500hp without cracking down the lifter valley)
For another example you can make about 500hp out of a n/a DOHC 4.6L motor with a mild motor combo. Take an aluminum 4.6L block, have larger sleeves pressed in which increases the bore adding inches but more importantly seriously unshrouds the valves! With a few other mods it is very easy to make 500hp out of 5.0L with this motor and run on pump gas.
Also, if you do that same "large bore" modification to an otherwise stock 05 Mustang GT 4.6L 3-valve hp would jump from an actual 320 (rated at 300 by Ford) to about 350hp on 87 octane gas! In truth you should make considerably more than that but I like to be conservative. If you contemplate doing this same mod to a long stroke (5.4L block) you would end up with a 6.0L motor that made about the same hp and more torque than the new C6 Vette 6.0L LS2 on 87 octane gas!
For reference show me an LS1 based motor that can make 350hp out of 5.0L in production trim on regular unleaded. We will be waiting a while, because GM has yet to make one that even gets close to that number in that kind of trim. Even GM's 6.0L LS2 needs premium gas to make 400hp, and that is with another liter of displacement.
Sooner or later GM wil move to multipile valves out of necessity. The LS series motor is very nice, but it is about as far as you can develop the pushrod too. The mod motor is still relatively new, and when GM does move to OHC's accross the board they will be several years behind in engineering.