To be fair, there was 5 years between the team Chia inherited and the one that won the cup. At that point Boston was at it's lowest perception wise as it had been in quite some time (and that's saying something). How much did Chia have to do with the draft, can you truly say he inherited guys like Chara, Savard, Kessel, Lucic, and Marchand? I wouldn't, I wasn't his biggest fan but there is more then enough reason Chia had his hand in all those picks and signings. Boston isn't going to go to the trouble of bringing him in then allowing their temporary asst GM to build the team before he even gets here, not without some input from the man.
http://www.boston.com/sports/touching_all_the_bases/2013/02/does_peter_chiarelli_get_enoug.html
The core Chia truly inherited imo was Bergeron, Boyes, Murray, Axe, Stuart, Thomas and Raycroft with prospects like Karsums, Versteeg, Kalus and Krejci.
He turned that into a cup winner.
Sweeney is inheriting the far better core in my opinion, more aged and higher paid or not. A lot of this core still holds big time value (Chara, Krejci, Bergeron, Lucic, etc...). No reason he can't deal with the cap issues and return value as well. Chia wasn't perfect, not in the least (Seguin and Kessel trades were Thornton'esque), but he performed a miracle when he was here.