I had a '98 5th Gen for several years and 130k miles, an '08 6th Gen for 79k miles and have had 2 Mk2 VFR800X Crossrunners (same engine as 14+ VFR800F) for 50k miles so I do feel qualified to to have an opinion on them wrt each other, even if I'm not that technically minded.
The 5th was love within the first 1/4 mile of riding it, that engine! Wow, blew my mind after not riding for a number of years. But it has always looked a bit 'overweight' and bulbous, certainly compared to the 6th Gen and had plenty of issues especially in the early days. I grew to love the looks of the 6th, especially the stacked headlights. It did everything better than the 5th.....except the engine. The VTEC was unrefined, even in an 08 model although fuel consumption was better and the VTEC rush when it kicked in was nice but it would have been nicer to have the smoother torque curve of the 5th without the torque drops preceding the VTEC kick. Handling, braking, looks (in the eye of the beholder), lighting were all better. But the VTEC was a technology looking for a reason to exist. Only introduced to meet emissions regs and it threatened to ruin a great engine.
Fast forward to the 2014 800F / 2015 800X and you have the best 800 of all imo. Honda have refined the VTEC engine significantly and the rest of the bike is as much an upgrade as it was from 5th to 6th Gen. I'm sure any 800F owners would agree as I've only ridden the 800F once but I have absolutely loved my 2 800X's and wouldn't swap them.
Having said all that, I do own an '01 5th Gen too.
The VFR1200 is the best VFR ever made. 😉