Sounds like the outdoor speakers can't handle as much power as the inside ones. Remember that the volume level on the iPod is the input to the main amplifier, so a higher volume on the iPod results in exponentially higher volume going to the speakers.
The outside speakers that came on my TT were the cheapest junk I have ever seen. They were flush mounted on the side of the TT and I had a hard time finding replacements that would fit because most decent speakers require a 2 1/2 - 3" mounting depth and the walls are only 1 1/2" thick.
I finally went with these
Poly Planar MA-905 marine speakers. They are component speakers with separate woofer and tweeter, and the woofer mountes in the recess where the factory speaker was. The stick out about 1" from the side of the TT.
I added a Kenwood 200W power amp between the main amp and these speakers, and now I get some serious volume. With the cheap Jensen OEM stereo, the Kenwood amp puts out plenty of power without distorting and the speakers can handle the power. You get decent bass from these, but you're never going to get any real bass out of a marine speaker without a subwoofer. The TT came with a powered sub inside, but I have not connected one for outside use yet.
I've had the speakers for 7 yrs now and they are holding up great. What's nice is that I can leave the speakers on very low volume in a CG, and the awning deflects the sound down. When out on the beach with no neighbors, I can crank it up and hear it 100 yds from the TT.