Intrigued to hear what you might think the difference is? Never having seen the distinction applied in that way, I had a shufti & the use of H1/E appears to spring from computer games. The closest I can imagine was the VK4501 having that 'H' for Henschel applied during prototyping to make it distinct from the Porsche effort (and the speculative H2). Once it had 'won', the E came in purely as a designation. Details slightly altered over time, as with anything else, but not really distinct types.
The Tiger H differed to the E by using rubber-rimmed road wheels and a larger Commanders cupola which made it very easy for them to be knocked out if hit in the cupola. So the Late version the "E" used a shorter cupola and had steel-pressed road wheels. Got that from a book by pen and sword the "Tiger" where it talks about all the different types of tanks based on the Tiger.
All in-service Tiger 1s were 'Es' (in fact, pedantically; from a certain point in '44 they were just 'Tiger' at Adolf's insistence.) There's no distinction in nomenclature associated with production variations. H was a prototyping distinction, not an Ausf./model. I got that from years of trying to understand Tiger's history, but I'm over it now. (Who's the book by? There's a few P&S Tigger tomes.)
It is by Anthony Tucker Jones, got it £3 in a sale when it was £15 from theworks.com I get your point about the Tiger. Just thought to point out the differences from what I knew. I am still learning though.
There's a fair amount of cynicism about re that author among the more serious panzer chaps. Not read any so won't comment, but I respect the opinion of some of those cynics. As Owen says, we're all just picking away at things. My personal recommendation for a good quality accessible Tigger book is the Haynes Manual. Often turns up in The Works for £6-7, and lays out the stall pretty well from assorted good sources without the substantial cost that can go with technical vehicle-specific books.
I guess there is a lot of cynicism about lots of historians. I will remain committed to try and learn all I can about tanks in my lifetime.