Agreed - but the OP would not have wanted Type 2 if he was just after 1 private key (and stated as much).
When I say "Accounts" I don't mean private keys. I mean separate branches of the Type 2 tree that can be separated in the Wallet software as separate wallets, but still be recovered by the same seed.
There is a paper that was published showing how Type 2 keys (even when hardened) are not as secure as Type 1 - I have not seen a satisfactory reply to this paper yet (although I don't claim to understand all the details in order to judge it's merit myself).
This paper was basically stating that "Because the purpose of Type 2 was to make it easier for auditing by giving people MPKs of individual branches of the hierarchy etc... it leads to over-exposure of many MPKs at many levels, and therefore increases the risk of being compromised... in comparison a Type 1 will only have ONE MPK, and exposing that gets rid of all financial privacy, so people will probably protect it more."
However, mathematically the weakness is exactly the same. Any MPK at any level in the hierarchy combined with any private key from any branch below that MPK can leak the master private key that corresponds with the MPK.
The only difference is that Type 1 lowers your exposure by not allowing for advanced auditing features (which could temp you into giving away sensitive information)
