Yes, you will always lose quality when converting formats. Regardless of
the types of files or their bitrate. (Well, unless the original avi is
lossless.)
The los in quality may be acceptable or even imperceptible, but it'll still
be there.
As for 'avi'...
Comparing bitrates etc. isn't too effective. You need to know what codec
was used with that avi.
If you use cinepak, indeo, or some other old codec for avi, then you may
need more bits for it than for mpeg-2.
As for newer codecs, such as Divx, xvid, and other mp4 based codecs, from
what I understand, they generally give about 10%-25% better compression than
the best mpeg-2 encoder. (This is in contrast to what many people say. I
often hear that it's twice as good as mpeg-2, etc. It's not that good.
People think that because they take a high quality dvd and convert it down
to 700m for a cd, and are still happy with the quality. That says more
about the quality of the source and their inability to notice (or care)
about the quality loss. When you are used to watching a dvd on tv and then
watch a mp4 of it on a computer, it can appear to be similar.)
Some avi codecs are 'raw'. They store the exact bit representation. So
there's no problem with converting them to any other format.
Some avi codecs are designed for slightly lossy but fast capture. Such as
mjpeg, which stores each frame as a sequence of jpg images. Very fast
encoding, but takes a lot of space. (This is often used for real-time tv
video capture on older hardware when using things like the ATI TV Wonder or
WinTV.)
I can't help you with other specialized avi codecs such as vp6, etc. etc.
And a final comment about the mpeg-2 encoder.... You might want to remember
that a lot of the final quality you get depends on the quality of that
encoder, not the quality of the source material. There is a very wide range
in quality in encoders. Today's best mpeg-2 encoders are much better than
the best from 5 years or the average ones still available today.
Other factors will effect the final apparent quality. Resizing,
interlacing, frame rate conversion, resolution (lines) changes, etc.
The audio compression used in avi is in a similar situation. It'll depend
on what format was used. Some of the older ones are quite bad. Suitable
for voice but not much else.
So, basically, you need to know the real quality of the source. What codec
was used? How good was it? Etc.
Most people just try it and if it's good enough, live with it.