I would like to make a note that the reason why TSE updates less frequently than TS may be related to the other tools included in TS; it may just be that the registry cleaner, system updater, etc, are the elements getting these additional bug fixes, so maybe TSE is not really outdated at all. I can't confirm it, but I highly suspect that to be the case.
My recommendation is for TSE. I think it has a smaller impact on performance, plus the protection it offers is more comprehensive, as has been shown frequently by cruelsister. The one thing I really like in Avast is its program updater, which works very well (it can update Flash, for example, very fast and conveniently).
I would recommend having BD and Avira engines installed but not enabled for real-time protection, this way you'll have optimal resource usage, plus the possibility of scanning with two powerful additional engines.
But Avast is not a bad option either. You could trial both for a week and get a feel of them. In terms of ads, TS (I'm not sure about TSE) shows some on its interface, and I've seen a pop-up offering to log into Facebook from it. But that hasn't reoccurred, and these ads are not intrusive. Avast is a little more aggressive, sometimes showing ads and other pop-ups offering their paid options.