I think the logos are used concurrently since we saw the old logo and also the sleeker, more modern logo (it's on the SHIELD Helicarrier bridge) in TA. It's kind of like how most athletic teams have a primary logo and then a secondary logo.
You may be right. IM2 had the old logo during the Fury/Stark scene at the end and then The Avengers went to the modern logo. Agents of SHIELD is going back to the old one, so maybe both are in use at the same time. Seems a little weird but not really a big deal.