You did not mention when you would be going, but you would NOT want 3 childeren at Mountain Vista in a one bedroom. You would HAVE to get a 2 bedroom. Even the premium one bedroom is kind of small with hardly any storage space. So, that may help make your decison. We stayed at Mountain Vista in March 2006 and it was getting a little worn. So, I would not consider age of properties at this point. I like the layout of Lakeside better the Mountain Vista. The two bedrooms at MV are lock outs, plus with Lakeside the use of the Avon rec center would give your kids lots of fun things to do.
One word of caution - if you stay at Mountain Vista be sure your room does not face 1-70. It is VERY loud at all hours, ask for the back side of the hotel, even if it is a corner room. Either property will be nice, there is also construciton of the Avon Gondola - which is fairly close to the Mountain Vista. You could call the hotel or check the Vail web site to see when this will be completed. Bascially either one will work, as long as it is a 2 bedroom.