If the are all (PA, SM (studio monitor), HF (Hi Fi)) perfectly FRFR (Full Range, Flat Response) at all volume levels then no difference at all.

But they are not because they are for different applications.

The PA speaker is intended to be used loud because the whole point of it is to project sound into a large area - my FBT Maxx 2A are supposidly capable of outputting 121 dB SPL (Sound Pressure Level) at 1m which is at the Hearing Damage Possible sort of level (intantaneous - for long term listening you can get damage at 85dB).  I have two and they sound great at what I think is a reasonable volume, but they are not intended to be used at low volumes, so at home in the evening with the kids in bed when it is all turned down they don't sound so good and I switch to headphones.  Fletcher Munson comes into it of course and I can do some limited adjustements using the built in tome controls, but the 10" woofer just doesn't move properly at lower volumes.  The PA Speakers also tend to be quite large - smaller than a 4x12 Guitar Cab obviously, but larger than SM or HF.

If you are only going to play at home then the PA Speaker is a waste of space and you will not be using it in the intended operating range so sound quality will be compromised.

The Studio Monitor is intended to give the perfect FRFR so that it can be used as a reference, but of course while it might be good and close to FRFR in an anechoic chamber when you stick it in a room you get resonances and echos and FRFR goes out of the window unless you have spent time treating your room.  That said it will be a lot better than the Home Stereo because FRFR was generally not a design objective for the average (or not so average Hi Fi) - the intention was to give a "good sound" in an average untuned listening environment. Which means that to give the illusion of volume (the Fletcher Munson effect) it will probably push the Bass and Treble levels up. Compared with the HF and PA the Studio Monitor is intended to give a really flat response so that everything can be heard, and it can probably go louder than the HF without distortion.

So which is best with a Pod HD?  It depends.

It depends on:

      1)     your ears and how good they are (mine are fairly rubbish due to years of miss-use)

     2)     room treatment - in a rubbish room everything will sound rubbish

     3)     whether you care how accurate the sound is

     4)     what volume levels you are realistically going to use

     5)     how portable you want your Pod patches to be

If you are happy with your Home Stereo sound and are not planning on going rock concert loud and will only ever use the Pod in that environment then just use the Stereo, and tweak the patches so that they sound good and inspire you.

If you have better ears and appreciate hearing fine details and can treat your room a bit (or work with a near-field arrangement) then upgrade the HS to the Studio Monitors - if you don't treat the room you will not get the benefit of the higher quality so look seriously at heavy curtains, bass traps and similar options to dampen the room.  Your patches will be much more portable, but you might discover some of the music that you used to think sounded great isn't quite as good as you thought it was.

If you have aspirations of getting onto a Stage at some point then Home Stereo and Studio Monitors will just not cut it with a live drummer and heavy bass player.  You probably won't hear yourself at all - the "100w" home stereo was that "peak music power" or "RMS", and how much of that power can you actually use without distortion?  How efficient are the speakers? 100W sounds a lot but my Home Cinema receiver puts 100W RMS into each of the 7 channels (so 700W into the Satellites + the seperate 12" Sub is about 900W); the speakers are accurate but relatively inefficient.  It can get really loud but at the same time it doesn't feel like it because it just doesn't distort (you only realise how loud it was when you try to talk to someone), but it is intended to push the sound into a relatively small enclosed area and that nearly 1000W is nothing sound wise compared to the mere 500W (2 x (200W + 50W)) of the PA Speakers.  The PA Speakers while they shift a lot more air than the HiFi and can project into a much larger space, are actually rubbish when compared with what my old Marshall 4x12 Cab linked to a 50W valve head could do - now that combination can shift the air around, not clean, not FRFR, but LOUD.  Shame that I just never got to play the Large Auditorium Gigs where it could be used properly - and that is why I don't have it anymore; it is intended to fill a concert hall not a pub and certainly not a home studio or bedroom.

My compromise is the PA Speakers which are great on Saturday mornings and the Kids have gone out to Ballet so there is no volume restrictions (apparently it is quite loud on the street), and headphones for lower level listening.  I do have Nearfield Studio speakers (i.e use them to listen close up) but somehow never use them.  When I play live they will be backline for small gigs and personal monitors for large gigs - the full PA can do its job in the latter situation.

If I wasn't intending to play live again and only played for fun I would probably hook to the Pod HD to the Home Cinema (i.e. decent Home Stereo). 

If my Home Stereo isn't really that good and I was writing and recording and wanted the best quality output I would consider the Studio Monitors.

There is no right answer and no wrong answer.  It depends on music style, realistic volume levels, aspirations, 3rd party factors (paper thin walls to the neighbours) and of course budget.

I'm trying a Mackie Thump TH-12A.  I may try the Alto 112A as well, just to compare.  So far, so good with the Mackie.  I am adjusting all my patches while playing through it and starting to get the HD500 dialed in (finally).  My Fender cleans and DrZ tones are getting there