Here is the info:
General
Complete name : F:\iphone pics & video\IMG_0034.MOV
Format : MPEG-4
Format profile : QuickTime
Codec ID : qt
File size : 22.4 MiB
Duration : 11s 87ms
Overall bit rate : 16.9 Mbps
Recorded date : 2014-05-18T12:32:51-0400
Encoded date : UTC 2014-05-18 16:32:51
Tagged date : UTC 2014-05-18 16:33:02
Writing application : 7.1.1
Writing library : Apple QuickTime
Model : iPhone 5s
Make : Apple
com.apple.quicktime.creationdate : 2014-05-18T12:32:51-0400
com.apple.quicktime.model : iPhone 5s
com.apple.quicktime.software : 7.1.1
com.apple.quicktime.make : Apple

Video
ID : 1
Format : AVC
Format/Info : Advanced Video Codec
Format profile : High@L4.1
Format settings, CABAC : Yes
Format settings, ReFrames : 1 frame
Format settings, GOP : M=1, N=30
Codec ID : avc1
Codec ID/Info : Advanced Video Coding
Duration : 11s 87ms
Source duration : 11s 107ms
Bit rate : 16.8 Mbps
Width : 1 920 pixels
Height : 1 080 pixels
Display aspect ratio : 16:9
Frame rate mode : Variable
Frame rate : 29.970 fps
Minimum frame rate : 28.571 fps
Maximum frame rate : 30.000 fps
Color space : YUV
Chroma subsampling : 4:2:0
Bit depth : 8 bits
Scan type : Progressive
Bits/(Pixel*Frame) : 0.271
Stream size : 22.2 MiB (99%)
Source stream size : 22.3 MiB (100%)
Title : Core Media Video
Encoded date : UTC 2014-05-18 16:32:51
Tagged date : UTC 2014-05-18 16:33:02
Color primaries : BT.709
Transfer characteristics : BT.709
Matrix coefficients : BT.709

Audio
ID : 2
Format : AAC
Format/Info : Advanced Audio Codec
Format profile : LC
Codec ID : 40
Duration : 11s 85ms
Source duration : 11s 122ms
Bit rate mode : Constant
Bit rate : 64.0 Kbps
Channel(s) : 1 channel
Channel positions : Front: C
Sampling rate : 44.1 KHz
Compression mode : Lossy
Stream size : 85.9 KiB (0%)
Source stream size : 86.1 KiB (0%)
Title : Core Media Audio
Encoded date : UTC 2014-05-18 16:32:51
Tagged date : UTC 2014-05-18 16:33:02

and also

General
Complete name : F:\iphone pics & video\IMG_0521.MOV
Format : MPEG-4
Format profile : QuickTime
Codec ID : qt
File size : 15.7 MiB
Duration : 7s 382ms
Overall bit rate : 17.9 Mbps
Recorded date : 2014-11-02T10:17:52-0700
Encoded date : UTC 2014-11-02 17:17:52
Tagged date : UTC 2014-11-02 17:17:59
Writing application : 8.0.2
Writing library : Apple QuickTime
Model : iPhone 5s
Make : Apple
com.apple.quicktime.creationdate : 2014-11-02T10:17:52-0700
com.apple.quicktime.model : iPhone 5s
com.apple.quicktime.software : 8.0.2
com.apple.quicktime.make : Apple

Video
ID : 1
Format : AVC
Format/Info : Advanced Video Codec
Format profile : High@L4.2
Format settings, CABAC : Yes
Format settings, ReFrames : 1 frame
Codec ID : avc1
Codec ID/Info : Advanced Video Coding
Duration : 7s 382ms
Bit rate : 17.8 Mbps
Width : 1 280 pixels
Height : 720 pixels
Display aspect ratio : 16:9
Frame rate mode : Variable
Frame rate : 120.163 fps
Minimum frame rate : 120.000 fps
Maximum frame rate : 126.316 fps
Color space : YUV
Chroma subsampling : 4:2:0
Bit depth : 8 bits
Scan type : Progressive
Bits/(Pixel*Frame) : 0.161
Stream size : 15.7 MiB (100%)
Title : Core Media Video
Encoded date : UTC 2014-11-02 17:17:52
Tagged date : UTC 2014-11-02 17:17:59
Color primaries : BT.709
Transfer characteristics : BT.709
Matrix coefficients : BT.709

Audio
ID : 2
Format : AAC
Format/Info : Advanced Audio Codec
Format profile : LC
Codec ID : 40
Duration : 7s 382ms
Source duration : 7s 430ms
Bit rate mode : Constant
Bit rate : 64.0 Kbps
Channel(s) : 1 channel
Channel positions : Front: C
Sampling rate : 44.1 KHz
Compression mode : Lossy
Stream size : 57.1 KiB (0%)
Source stream size : 57.4 KiB (0%)
Title : Core Media Audio
Encoded date : UTC 2014-11-02 17:17:52
Tagged date : UTC 2014-11-02 17:17:59

You say that you have Quicktime, which is necessary to play MOV files in Vegas. I have heard in the past of some incompatibility between Vegas and later versions of Quicktime, but forget the details and don't know if it is still an issue.

The videos have variable frame rate which may be a problem. Also the second has 120 fps which may also be a problem.

Hopefully somebody with more knowledge of handling these file types will chime in.