There is a massive difference between the two. I don't know why, there just is. The 2605 is way brighter and quite harsh, the 1605 is fuller. To be fair I like both of them and live obviously the differences aren't so pronounced, I just felt not much point having both, although I might just end up keeping them anyway.
My 1505 was my favourite when I got it, then it went back, then my new shuker was my favourite when I got that, then the 1505 came back and not sure. I played at a practice for a gig that didn't happen though and the 1505 really shone. However, the shuker is still the looker and great to play, as long as you don't want to dig in. The EHB is more the angry kid on the block.
But the other day I picked up the 1605 to play something and.. you know, like a favourite old pair of slippers?
The EHB doesn't have big singles though, even if they look the same, it has big splits. Truth to tell it is not a lot of difference although they are humbuckers which means I can get near the valve amp.
The variable mid is certainly better than the switch, on the 1505 (and on the original 5005 and 1000) and a bit easier to find what you are looking for.
And also makes it easier to use with the shuker that has similar (but not the same) layout