The past can be considered more secure, but the attacker could fork at the current block, spend coins on the public block and save them in his own.
I wrote about security of transactions in a scenario where the attack starts after the transactions were confirmed and attacker has limited time on hand.
I think that the scenario is of practical relevance:
Assume that the checksum of a company's book is regularly committed to the Bitcoin block chain. The CFO learns that an error was made with a time lag.
The question is if he can camouflage it by buying 50%+ mining capacity for a short period of time, that he can afford.