a tall order i will try to accommodate.
first off the two are considered moderate to easy climbs although i heard less traveled routs on lanin can be tricky.
out of the two the easiest to get to and climb is villarica, it is right out side pucon(you can arrive in pucon and the walk up is well established) no route finding or any such mountaineering skill needed other than glacier travel and especially self arrest techniques.
as well i believe the views around pucon are a better hit than lanin(mostly arid landscape).
the only draw back to villarrica other than the total lack of any technical climbing is the whether can be a big factor on the climb to much sun snow or rain could postpone summit push by a day or two(a mere 3h up 30m down due to the wonderful glissadding the volcano offers).
as for lanin it is a little tougher to get to and makes you're schedule harder to stick to unless you fly to bariloche than take a bus,
the summit of lanin is a 2 day push of scrambling and very light glacier walk to the summit but by far harder than villarrica and what i feel to be an upside to this volcano, it is not active thus once reaching the summit you dont take a gasp of toxic fumes like in villarrica.
in conclusion villarica easy to get to, quick ascent and fun descent, views are great and green with volcanoes all around the volcano is active if thats youre fancy and ,ost important you cna easly do this in youre time limit.
depending on youre experience level if still beginner would recommend guide service in villarrica and lanin both can be found in town at great expanse, lodging fairly cheap in both.
lanin is much more of a mountaineering experience,longer,more isolated and less visited, whether dosent play a great role on summiting
you do have to pay a small fee in the border cross to my recollection but its a beautiful boarder worth crossing if not for the volcano than for the scenery.
these links have all the info you might need eupiment,getting there,red tape guiding/transport services,bata etc. anything else you can ask when you get there, the people in the area are very helpful.http://www.summitpost.org/volc-n-villarrica/151480http://www.trekbariloche.com/treks/lanin-climb.phphttp://www.trekchile.com/volcano-villarica
the bus service in these country's are fennominal better than first class on a plain and way cheaper worth it, from BA to bariloche i think between 70$-110$ the expensive one is a bed on the bus.