While Ancestry is not about to disappear any time soom, it could happen. More likely their system will overload or your ISP will go down. If you can live with these disruptions to the access to your database go with the online tree. If you know you will only be working on your family. (writing stories, ect) where you will aways have internet access go with the online tree.
However if you go to cemeteries, go to the location of family residence for pictures, visit relatives with questionable internet access, etc. Go with the main database on your computer.
For myself I like having all of my documents (I download everything and scan the rest) and my data on my computer. I can go out in the yard beyond my wireless and work in the shade on nice days, I can take it to the cemetery and check the tombstone information against my database. I don't have to worry which corner of the library I find the books with my information. If I am in a hotel, I am not dependent on their system, nor do I have to worry about getting on a secure network.
As you can see for me there are many incidence where the
internet is unavailable, so I can work anyplace I go.
If you are asking me, then keep everything on your computer, back up your database to one of your other computers or your external hard drive (They are cheap now days) and if you like put your data online as a tertiary location of your information.