Hey Daniel, and welcome to the forum. I listened to the files and from what I can tell, the main difference is that your mic recording is picking up the complete sound of the violin and all the advantages of an acoustical instrument. The bad part about playing with a mic is obviously that it will pick up the sound from everything else as well as your amplifier and you need to deal with feedback, noise and such.

As far as the transducer pick-up is concerned you are hearing more the sound of the strings and vibration instead of the true violin sound. I have a Zeta Jazz Fusion violin that cost about 6K when it was new 9 years ago and the sound is not better from that one. The jazz fusion is a solid body instrument with 2 piezo mics under each string meant to pick up more of the side vibration rather than the up and down motions. Each string level can be adjusted if you open the back as well but the natural no-effect sound from that fiddle is terrible.

The way to get a good sound from an electric violin is to use an effect processor, pedal or Amp with effects such as chorus and reverb. There are floods of effect processors available, and for most people a cheap all in one guitar box with pre-programed sound effects is more than adequate.

Bring your fiddle to a music store and test different effect processors and choose the one that you like the most and can afford. Check out the line 6 pocket pod which I've seen for under $100 and is small enough to have on your belt. Also check out Zoom multi-effect processors for as little as $50.

Great for the price. You'll have a lot of fun with that.

A tourte is a small rubber mute that dampens vibrations therefor softening the sound.
 

Probably better for you. The biggest difference between the two is that a guitar amp often has effects available for high-gain and overdrive to distort the sound, though the settings can be set for a clean plain sound as well.
Keyboard amps don't need that since they have effects built into them. Guitar amps tend to suit a fiddle well since they are designed for the frequencies that guitars produce and close to ours. Those same effects are pretty cool on the fiddle as well. By the same token, keyboard amps have a wider variety of frequencies including tweeters which the guitar amps don't have. If you play real high on the fiddle you are usually better off with a keyboard amp and guitar effect processor between.