I currently shoot a Toelke Chinook but have the urge to order a new bow and would like to try a longbow for the first time in my life.  If I were to go with a Pika, how would it compare to a Chinook?   What characteristics differ a longbow from a recurve?  Why would I like about a longbow?

Very similar, you will like it very much.

I have not had the pleasure of shooting any toelke models.   Can give you a generalization.    Modern reflex deflex longbows  will generally quite close in speed compared to a "conventional"recurve.  You should expect them to have little to no hand shock like a recurve.  They will be more quiet as  the string does not contact the limb.  It's much harder to torque the limbs of a longbow and the limbs themselves will be less "squirrely".   In the case of Pika it has a pistol grip so the grip won't be alien to you compared to an older straight grip.   The Pika is should also be very pointable due to the more forward riser.

I've owned both and they are shooters.  My go-to bow is a 56" Chinook (I have a 27" Draw length) and it is the best shooter I have ever owned.  I have had 2 or 3 Pika's and the only issued I have ever had is the release.  With the Pika being a shorter bow, your release has to be more consistent.  If you do your part, the Pika will do its.

Best of luck.

Just a heads up, I'd probably wait a few more days until Dan and Jared reveal what they have been working on these past days. 

Based on what I read in another thread, Dan and Jared will be coming out with a bow more suited for longer draw lengths. I was hoping for a 58" Pika myself but don't think that is in the works.

I have owned both and have owned quite a few Toelke bows. To me it is hard to compare these two models as one is a recurve and one a longbow. I would definitely shoot a longbow of some type first just to see if you like a longbow. I will say the pika to me is smoother in draw versus the whip. Really hard to believe a bow that short is so smooth. Mine was a 56" bow although I only draw 28". I have owned two very similar longbows of a different brand at the same time in the past and one was 54" and one was 56". I shot the 56" much better hands down. Neither stacked at all but I just don't shoot bows under 56" very well. So for me if I were to order a  pika it would be in 56". These bows are very light weight due to their size. I shot the pika best with a quiver to add some mass weight and the bow bolt takedown also added some weight. My favorite Toelke is the Lynx which is not made anymore because Dan said he and Jared neither one like making three piece bows. When I shot my Chinook and Lynx side by side I always preferred the Lynx. I think it was due to the mass weight and I liked the grip better on the Lynx.