Hi - For what its worth here is my 'transition' ....
Started surfing 8 months ago on a 7'2" Hybrid Funboard.
6 Months later I supplemented this with a Miller V-Skate, 6'6" x 20 3/4 x 2 3/4
The step down to this board was quite noticeable (needed to paddle much harder etc), but wasn't too bad due to the volume of the 6'6 being quite high.
The Miller snapped in 4-5ft sets last weekend

so I have just bought an Aloha AF2 Turbo, 6'6" x 19 1/2 x 2 1/2 - this is a big change from the Miller despite being the same length as it has much less volume in the nose, is noticeably thinner and quite a bit narrower. I honestly believe I would have struggled to go to this straight from the 7'2
(Incidentally I surf every morning for about an hour - sometimes get an afternoon session in too!)
Looking at your pics ... The first board does appear to have much more volume in the nose, but is also wider and thicker. I would say this would be the best of the two for you. Also, coming from a 7'8 is a big jump - have you considered moving to a 6'10 as an interim?
The second board still carries its width quite far forward, but being narrower and thinner will have less volume overall.
Personally, if these are the only two options I would go for the first one, however I would also think about trying one before you buy it to see how it feels and maybe looking for a 6'10 or simalar as a step-down board.
Finally - what kind of waves are you surfing and how often as this will have an impact too. The second board looks like it may be better in bigger waves and the first board would be a good board for 2 ft grovelling days! (Although you really need to look at the rocker too when thinking about board shape for waves)
Hope this helps!
Jonny