In regards to the gezeiras shaveh from succos to pesach, what other dinim do we learn? Is one required to be יושב בסוכה on his left side? How much does it have to rain on pesach to make you patur from eating matzah - just a drop, as that would make it gebruchts, and ruin it? Or is it just a מנהג לחומרה?
In both we have the custom of inviting invisible guests. Arguably Sukkot is more outrageous because we invite (and pretend we will feed) not one but seven different individuals. But only on Pesach do we not only open the door and pull up a chair, but also pour a cup for our exalted friend to drink -- all before relying on him to make halachic rulings for the seder.
We not only tell our children this when they ask, but fervently hope they will believe in it for their whole lives.
There are a number of connections in fact.
One of the reasons that we sit in booths is to commemorate how Hashem protected us while we traveled in the desert, which is why Hashem allowed us to bring dough -- because he liked us. As the pasuk says, מצה חן במדבר
Also, the last day of Pesach commemorates Kri'at Yam Suf. We learn that the last day of the Sukkot holiday is its own holiday, of Atzeret, because, in the same way, the last day is called an end: "Kri'at yom, sof."
One halacha learned from the גזירה שוה is that on both holidays we should do things that hurt us in some way.
Building the Succah tends to cause back or neck pain from lifting heavy boards or stretching the wrong way to put up schach. It also causes sprained or bruised thumbs from hammering nails. If you're lucky enough not to get pain from that, the lulav inevitably pokes you in a finger or your back or somewhere else that isn't pretty.
On Pesach, we eat horseradish that hurts the tongue and throat. Then, there's an abundance of matzah as well as loads of other food that hurts the stomach.
Just remember that all that pain is done for the sake of praising G-d for the gift of these holidays so that we can eat a lot and gain weight. Remember - there's no gain without pain!