From my experience, going from the Seminole to the Saab was both easy and difficult. It was easy in the sense that the same flying skills still apply. However, difficult in that the airplanes are two different monsters. The Seminole has it's own quirks regarding systems management and controlability, whereas the Saab has a completely different arrangement. The Saab is a heavy airplane, fast, and doesn't slow down easy on the glideslope. Above 210 knots and descending on the glideslope in the Saab, you don't have an easy chance of slowing down to gear speed of 200 knots. Especially on 4R at MDW with the 3.4 degree glideslope! I think it's clear that things move really fast in a faster airplane, but I always flew wanting more speed, so that wasn't a major issue for me in transitioning. I was always the one cranking down the ILS being told to slow for the King Air on final.
Besides the actual stick and rudder differences (which are minimal), the largest difference is standardization, resource management, and advanced systems management. You have a lot of things to pay attention to in the Saab. Watching ITT temps in the various stages of flight, completing the weight and balance and performance numbers in the computer and ensuring they are spit out correctly (you won't have a Vr of 110 at 28,500 lbs TOW... RED FLAG). Now flying with many different personalities, you need to learn also how to read that person next to you. It's important to get a sense of their comfort level, their approach to procedures and flying, and whether they read you correct or not. Learning how they operate changes your approach to flying with each trip. Same goes for the F/A in back. If she is new, takes time with things, etc., you might need to taxi a bit slower, call in back more, and what not.
Another hurdle is learning to properly use all the navigation aids to your disposal. We only have dual VOR/DME/single ADF, however using both NAV 1 and 2, DME hold, and fixing on an NDB can greatly improve your situational awareness. Knowing which EHSI mode to operate in depending on the equipment you are using (the ADF needle gets hidden depending on how you are being vectored while in ARC mode, better to use ROSE mode) is a big part of that situation awareness, as an example.
I think the best way to sum it up is that when you move on to a larger aircraft in scheduled 121 service, you'll find that there is a LOT more to flying than actually flying. Soon the stick and rudder becomes a subconscious thing, and you concentrate your immediate conscious psyche to handling ATC issues, looking for ATC shortcuts to get back on schedule after a delay, handling pax issues, and monitoring the various systems and automation on board.
One last thing: IFR skills are a MUST. You fly by instruments MUCH more in larger aircraft, and without a decent scan and the ability to interpret the instruments in front of you (possibly in a glass format you are not used to) you can get behind. When I was familiarizing some of our instructors at U of I in the B-737 LOFT sim, it was equipped with the same EFIS setup that our Saab has. The EADI has a bank indicator that is reverse of what is found in the Piper and Cessna series attitude indicators, and it was really screwing up the guys flying it who were so used to the alternative. It can be a challenge.
* If this doesn't make sense at some points, sorry, typing fast and didn't proofread