I wanted to find out that do passive PA speakers like PEAVEY PVX 12 sound better than home theater tower speakers. I wanted to upgrade my front satellites with good quality full size fronts. Please advice.
Yes they are often better but it depends on your taste. DSP is highly recommended for PA speakers.
The Peavey you list wouldn't be an ideal choice. There isn't any published data and the most important cause for concern is the high internal XO. IMO you would not be happy with this particular model.
I'd recommend some further research into other choices from Peavey,RCF,Behringer,EAW,Mackie,Turbosound,EV etc. It does depend on your budget but it may not be the best idea to get the cheapest PA speakers possible, to truly realize their benefits you must at least get into the mid budget ranges. Some cheaper options can be a very good value but you must search for them, look into Behringer and Mackie along with Peavey for the better budget choices.
Do remember sound is subjective so it is hard to say what will sound better to you, only you could decide that. That said PA speakers when correctly designed with appropriate components are capable of greater dynamics,clarity and SPL than home speakers. Do note that many cheaper PA speakers tend to suffer from a harsh top end, this often can (but not always) be corrected with DSP. For a budget DSP the Behringer DCX2496 is the best choice IMO.