Personally, I think the Gospels evidenced a revolutionary philosophy that questioned much of the concepts of the Old Testament or if not questioning the rituals, rules themselves, then pushing people into thinking about them a new way. Basically, to paraphrase, that the rules were made for the people and not the people for the rules. A philosophy that said the rules should never overshadow what they were meant to give.
Healing on the Sabbath.
Hanging out with the unclean, sinners.
The statement on kosher that it was less important what you put into your mouth than what came out of it.
Much of the Ten Commandments was "Thou shalt not..." (pretty
good rules, too). Much of the Christ commandments were "Thou Shalt....Love Thy Neighbor as Thyself, etc.
The inclusion of women as equals.
The Turning of the Other Cheek compared to the warlike Deity of the past.
I don't think the New Testament (Gospels, here only, I'm not a huge Paul fan) was a continuation of the Old Testament, but a challenge to it, a respectful challenge to it.
That being said, there is a strong correlation between practioners of both, and they could learn much from each other. There are beautiful rituals and philosophies on both sides and the intertwining of them cannot help but to lead to a better understanding of our own beliefs.
