What are the benefits in using a carboy for a secondary, rather than just using another 5 gallon bucket? I'm just curious because carboys are a pain in the behind to clean properly, and other than actually being able to see the beer itself, I'm not sure what the benefits are.
Other than being able to see your beer, as you pointed out, there isn't any benefit and like you noted, the drawback of cleaning a second container. I've brewed gallons and gallons in plastic buckets and don't really see the benefit of transfer to a secondary either. You're exposing your beer not only to nasties, but more oxygen too.
I nice cold crash before I bottle or keg clears my beer nicely along with whirlfloc at the end of the boil.
The benefits are that if you are lagering your beer for an extended period of time > 2 months, then it is likely that you will not want oxygen slowly permeating the plastic bucket and oxidize your beer. The glass is impermeable to oxygen in a way the bucket is not.
Being glass they tend not to scratch or degenerate over time, just don't drop it.
An added extra is they look amazing, but can be awkward unless you get a bendy brush to clean and tend not to have nice handles.
You've got a couple of options and they all have pros and cons.
Secondary fermentation in same vessel as primary
If your primary vessel isn't needed again and your main fermentation went well, you may not want to rack at all (if the recipe allows it). Especially if your primary vessel is a cylindroconical which means you can get sediments (dropped out yeast, hop residue, etc.) out. In that case you can avoid any chance of exposing your beer to oxygen while racking which is a big plus.
Secondary fermentation in glass carboy
Seeing your beer is nice but it doesn't really help with much. I also find it quite tricky to get larger hop bags in and out of some of the glass carboys. If you can choose between glass and plastic, of course go for glass. Plastic breathes, plastic is ok for milling grains and storing cleaning solutions but not for wort and beer.
Secondary fermentation in plastic bucket
If you ferment beer in plastic buckets, well honestly... stop doing it. Unless you're really on a very very tight budget or don't care for the quality of your beer too much.
Secondary fermentation in stainless steal
If you need a secondary vessel and don't have glass or your batch size is too large for glass carboys, stainless steal tanks are of course a great choice too. Glass can break and glass carboys are heavier than stainless steal buckets.