Both tanks are strong performers and share common electronics. That being said, the Tiger 1 OTB is a better performer. The stock tracks are stronger and the track tension adjusting system is better in the Tiger 1. There is a wealth of detail parts and add ons for both tanks. Depends on what you plan to do with him, IOW Sunday driver, detail competitions, or knock down drag out Infrarot competitions like at AAF Museum.
There is a great deal of knowledge on this forum. Some of the lads have been doing tanks for many years, and just about all of them are willing to share their knowledge. If you have any questions, just ask. Someone will answer generally rather quickly.
Here's two links to my sight. These links give you an idea of some of the items available for either tank.
http://www.etoarmour.com/products.php?ViewCategory=10
http://www.etoarmour.com/products.php?ViewCategory=9
With either tank, as I said you can go as little or as far as you want. Here's a pic or two of the inside of a Jagdtiger, King Tiger being the same. This one is heavily modified with reinforcements, hand made track adjusters, aftermarket suspension system, transmission brace and special eto produced competition transmissions.