I know sometimes people create patches for only 1 or the other, but when that is not the case is 1 preferred over the other? I am thinking about overall compatibility. Does 1 play better with other mods and patches?

I am not sure I understand your question, but this http://www.gamesas.com/topic/1354395-update-bsas-and-you/answers everything you want to know about bsa vs loose files.

So loose files always win over a bsa? I should prefer loose file versions?

Yes.

That really depends on what you are trying to accomplish. One of the nice things about bsa files is that they are inert unless they are activated with an esp file of the same name (or registered in the ini). So having the files in a bsa gives you a lot of control since you can make them win a conflict with other bsa files by simply loading their associated esp later, or you can deactivate their associated esp file to prevent the bsa file from being loaded at all. These features makes them convenient, since you can change your files around by simply switching load order of esp files and activating and deactivating them, rather than having to install and uninstall a bunch of loose files. If you want to make sure your files win all conflicts, than yes, install loose versions and they will win all conflicts, until you replace them with something else.

Very helpful thank you!

I prefer BSA's as loose files tend to get misplaced or overwritten over time. BSA's also load faster or are read faster (theres a comments by SMKviper somewhere or other where he mentions it). If a mod has loose files the first thing I do is put them into a BSA or two. I bundled up all my countless loose files (texture overhauls mostly) and put them into a few large BSA's. The game install folder nearly halved in size too.

Do use the archive tool that comes bundled with the construction set, or a third party tool? What compression ratio do you use?

If its just textures and meshes then BSAopt will do and usually compression setting around 8 is what I use. I don't know if there has been much research done aka read time vs compression ratio, if there is I don't know of it. BSAopt gives higher compression ratio's than the CK's Archive tool I believe.

If its sound files and/or scripts its probably better to use the Archive.exe tool that comes with that CK as they usually require Flags to be set in my experience, and sound files in particular do not need compressing and infact may not function correctly if they are.