I believe the chip hardware should be the same, just packaged differently. According to the 16F886 datasheet I have; DIP, SOIC and SSOP pinouts are identical.
When it comes to firmware it's usually the case that later versions work better than earlier but any change could cause a difference in operation. It's not unknown for a software upgrade to reveal problems in existing code which never exhibited themselves as bugs in the past. Obviously it shouldn't happen, and I'm not saying it has, but new firmware releases shouldn't introduce new problems but it can happen.
Can you give more detail as to what specific issues you are having, perhaps narrow it down to simple example code which works on the DIP A.2 but not on the SMT A.3 version ?
Do you have a DIP A.3 or an SMT A.2 version you could do comparisons with which would help indicate whether it's a related to firmware or related to packaging issue?