The video data is still, at its core MPEG4. There are different profiles, containers and such but the data is still roughly the same. Different data rates, encodings, etc for different platforms.
Here's a good article:
MPEG-4 - Wikipedia, the free encyclopedia
Basically we're all getting AVC on both Android and iOS. It's the most popular and both phones understand it. There may be differences as far as bitrates and resolutions supported but it's still MPEG4.
3GP is a container for MPEG4 that is mainly used for MMS.
This article has more info:
3GP and 3G2 - Wikipedia, the free encyclopedia
The choppiness is probably because of the extreme compression of getting video into the MMS format
Multimedia Messaging Service - Wikipedia, the free encyclopedia
Basically you have to compress it into 300-600k files which is insanely small for video.
Multimedia Messaging Service (MMS)
It's also not an iPhone specific thing:
Support MMS video quality - Android Forums
http://forums.crackberry.com/forum-f143/sending-videos-via-mms-video-quality-603329/
https://motorola-global-eng.custhel...l/a_id/39780/~/droid---sending-video-over-mms
And the stock video recorder outputs MPEG4 (.m4v, iirc) files. Even Quicktime's .MOV is MPEG4 at the core now.
Best choice for the OP would be to have their friend e-mail the videos or use another means other than MMS.