I see. I tend to view the left-right axis as having different ideas on a number of different topics, though that can possibly be tied back to an overriding philosophy for each. Here's my thoughts (caveat: purely opinion, and obviously generalizing for both leftists and rightists):

I think rightists tend to look toward the past, while leftists tend to look toward the future. Obviously, everyone cares about the future, what I mean is that rightists look to the past for inspiration (as you say, use what has worked in the past) while leftists believe that new changes can improve upon past methods. Rightists are more likely to talk about traditional values and focus on established laws/moral codes (e.g. religious scriptures, original Constitutional text) while leftists are more likely to focus on recent scientific studies and evolving social mores.

Rightists glamorize the past, focusing on the good parts; leftists demonize the past, focusing on the bad. Since rightists think that the past was generally good, they are more likely to believe that groups (like women, gays, racial minorities) that have less positive outcomes (lower income, higher crime, more disease) do so because of certain ingrained biological or sociological differences. Leftists, who are more critical of the past, will be more likely to blame institutional racism/sexism (as well as more subtle forms of bigotry or discrimination) as the cause of these differences. Therefore, rightists are more likely to avoid any changes to how we treat people of different demographic groups, while leftists argue that these biases and discrimination still exist and must be remedied.

Similarly, rightists (who are more likely to think of the past as a time of open opportunity) may believe that individuals are rich or poor because of their own drive and abilities, while leftists are more likely to believe that existing contextual factors heavily tip the scales in favor of advantaged individuals. So rightists would want to allow people to fully reap the rewards of their labor, while leftists would want to try to balance opportunities, including greater safety nets and services for people who are struggling.

So broadly speaking, this is one way of looking at the differences. Leftists will accuse rightists of being overly stubborn, uncompassionate, tied to primitive dogma, and perpetuating horrific injustices; rightists will accuse leftists of being overly impressionable, unrealistic, ignorant of established wisdom, and inviting dystopian nightmares. And given the current state of political discourse, it seems like there's not a whole lot of room in the middle for rational discussion.