Back in the 1700s and 1800s rye was quite common and popular, corn came on later which are the bourbons. Bourbon whiskies are usually sweeter and sometimes smoother, rye is a little fruitier, sometimes spicier and usually drier.
Since you said you liked white whiskey I figured you had come across some made the old fashioned way. Rye seems to be making a comeback and there are some good ones out there, you should try one sometime. Next time I go to Kentucky I plan on stopping at the Buffalo Trace Distillery, taking the tour and buying some of their White Dog Rye Mash Whiskey (125 proof).
I used to be a rye drinker exclusively, except for vodkka of course, till i got into scotch. I just love the stuff. Mostly the peaty smoky stuff. It can be quite vile and yet very smooth as well. A real taste extravaganza!
I scorned the popular stuff, like glenfiddich 12, but had a glass handed to me and as it was free i drank it down. I realized, strictly only for my taste, a cheap scotch is better than a good rye. I haven't been properly educated on bourbons so perhaps I'm missing a treat there.
I used to drink Scotch at one time but haven't in the last 10 years or so, still have a 1/2 full bottle of Glenmorangie 18 in the cabinet.
The only way to see if you like bourbon is to buy some and mix it with a few different things to see if you like it. Since it seems like you have somewhat the same tastes as I do try some Buffalo Trace or Evan Williams, since neither is that expensive, and see what happens.
As far as the rye goes I've been drinking Bulliet or Knob Creek lately.