Help matching different frame rates

I'm very new to FCP. I'm used to using iMovie which was easy and FCP seems as well but I can't get 2 different clips of the same shot (different angles) to match for picture in picture of a fitness video. It's a 40-minute clip and when I line up the 2 at the beginning, by the end, the PIP is several seconds off.

One camera is Sony NEX VG20 shooting at 60i, and the others are Flip (2 different gens, one shoots at 30 fps, the other at 60 - doesn't matter which Flip I import from, neither match up).

FCP says the Sony cam is at 29.97 which is weird since I'm shooting at 60i at highest quality, 1920x1080. It has the Flips at smaller quality but 30 or 60 fps as they are. I set the project to use the settings of the first clip (the sony), but the Flips aren't matching. I've tried getting the Flips to Fit and Fill the project frame rate but it does nothing.

I wanted to use FCP since I'm trying to get this onto a DVD with great quality that iMovie can't do, I just need this one thing corrected and I have a feeling it's an easy answer that I'm not seeing. Any help? Thank you.

60i is 29.97fps. 30 and 60 can be 30 or 29.97, and 60 or 59.94. The drift is more likely due to audio sample rates.

Is there any way to change it so they match? Or do I have to go back to iMovie?

You may need to convert the material but without knowing complete specs of the media it's hard to say. Was the material optimized when it was imported?

If you're more comfortable with iMovie and need to get this done, then that might be the place to do it, until you learn how to use this application.

The Flip is at 44.1 and the Sony is 48. I tried to change the project down to 44.1 but no difference. I've tried deleting and reimporting under different settings several times but no change. On second thought, I can't use iMovie because it can't export to DVD quality. Any help is much appreciated.

The Flip media needs to be converted. Open one if the Flip files in the QT player and report its complete specs from the movie inspector.

Did you optimize on import?

Do you have iDVD?

Yes, I optimized on import. I can delete and reimport if necessary.

Yes I have iDVD.

Flip specs:
Format: AVC Coding, 1,280 x 720
AAC, 44100 Hz, Stereo (L R)
FPS: 60
Data Size: 3.11 GB
Data Rate: 9.89 Mbit/s
Current Size: 1,280 × 720 (Actual)

The Sony specs from the Original Media folder of FCP, if you need them:
Format: H.264, 1,920 x 1,080
Linear PCM, 16 bit little-endian signed integer, 48000 Hz, Stereo (L R)
FPS: 29.97
Data Size: 7.04 GB
Data Rate: 22.61 Mbit/s
Current Size: 1,747 × 983

The Flip file is .mov or something else? This has been optimized? Can you check what the specs are for the High Quality media for this.

Try using Compressor or MPEG Streamclip to convert this to QuickTime in ProRes with uncompressed 48k audio. Make the frame rate 59.94fps.

Sorry, I chose the vid from Flipshare, this is the flip vid after optimizing:

Flip specs:
Format: AVC Coding, 1,280 x 720
Linear PCM, 16 bit little-endian signed integer, 44100 Hz, Stereo (L R)
FPS: 60
Data Size: 3.54 GB
Data Rate: 11.17 Mbit/s
Current Size: 1,280 × 720 (Actual)

I'll look into those programs