I've done both and really haven't noticed a difference. I usually ferment in a bucket, but I only have one, so on the rare times I have a second batch going at the same time I primary in a carboy. A 3 gallon batch in a 5 gallon carboy is plenty of headspace for blowoff. I have a 3 gallon carboy I use for secondary.
I have both plastic and glass, but I only use the glass if every other vessel is full. It's heavy, it's hard to clean, and I know one of these days I'm gonna break it. The plastic ones also have a wider mouth (#7 cork) vs the glass one (#3 cork) so easier for siphoning. The glass ones mouth is just barely big enough for my auto siphon. (The glass one was given to me free, I bought the plastic ones)
In my opinion you can do either/or.