Yes, SSD's are the faster in Read/Write access but at a price. The amount of storage they have is less than HD's and are costly.
And yes, SSD's are quieter than HD's. But most of the issue is dependent on what you are doing. Running heavy CPU/Graphics applications are big creators of heat which then causes the fans to fire up to full cooling which I suspect is your noise issue not the heat of the HD alone.
As to which is the better direction going with a straight SSD Vs a SSHD?
A SSHD gives you a more balanced solution by combining both the SSD and a HD into a single hybrid drive. So you gain the speed of the SSD and the storage space of the HD.
At one point we took the optical drives out of our laptops so we could add in a second drive (SSD) to gain the the speed of the SSDs and still have the storage space a HD offers. Now with SSHD's we get it in one device. All our non-retina Mac Book Pros have since been upgraded to SSHD units.