My question is, I have two of these amps http://www.shopping.com/xPF-Kenwood-KAC-829 and both are bridged.

Amplifier Type Dual Channel
Bridgable Bridgable
RMS Power at 4 Ohms 100 W x 2
RMS Power at 2 Ohms 150 W x 2

Would running this subwoofer be reasonable? or will it be underpowered?

10" subwoofer with dual 4-ohm voice coils
power range: 50-300 watts RMS (150 watts per voice coil)
peak power handling: 900 watts

http://www.crutchfield.com/S-qEkoc9h...SWS-1043D.html

Right now I'm running a 10" Rockford P3 which is underpowered by about 100watts RMS. I just don't want to make the mistake of buying a wrong specification subwoofer again lol.

Any suggestions on what I should look for if the subwoofer above does not work?

 

Dual 4 ohm voice coils are a nogo for you with either amp. You need a single 4 ohm or dual 2 ohm (wired in series to 4ohm) to properly match the amplifier.

Suggestions on a new sub are going to be limited to your budget and if you are changing the box that it is mounted in (this will make or break the output of the sub). Want loud, Digital Designs, www.ddaudio.com

 

^^^ Agreed.
simply switch to this model Alpine Type-S SWS-1023D 10" Dual 2-ohm Component Sub
And you are good to go - your amp should do 300wrms bridged and that is perfect.

 

With my current set-up. Can I run two of those without issues?^

I found the Alpines near my place!

 

Those = ???
two of the dual 2 or dual 4?

With your current amp, you can run two Dual 4ohm subs on one amp.
Wire the subs parallel, and that will give you a 2ohm load on each channel. The shortfall - is each sub would only receive 150wrms. To really make a sub sing, you should match the sub with an amp that can produce 80% - 120% of the sub's RMS. So you're best off to get the Dual 2

If the Dual 2ohm that I noted in my previous post is what you are saying is available, you can wire the coils in series to get a 4 ohm final load. Your amp will give it the 300wrms it needs to reach it's full potential . . . and if you have 2 of those amps, you can use each amp to power its own sub for a lot better performance.

As mentioned before you will be best off to get a single 4ohm or dual 2ohm for your application . . . really 150wrms isn't much for a sub - so look for a sub that can maximize the potential of the amp