Although the implied version increase that comes in the names of those two protocols might suggest something better in IPv6, I will once again reiterate that things are just different.
Much has been said about the physical differences in the packets and one can look them up if they want to see them. I just want to focus on a few points.
Quality of Service in now deeply embedded in the packet in two fields, traffic class (sometimes called priority) and flow label. This allows routers to more efficiently handle packets according to some sort of administrative schema. There is no real need for routers to guess at how the packet should be handled. This essentially replaces the ToS field of an IPv4 packet, which is currently used to provide QoS through Diffserv.
Pre-1998, this was very, very important to network connections which were often overwhelmed, even then, with the various types of real-time vs. best-effort data streams. Today, you get bandwidth fire-hosed at you, so there is less and less of a need for this the closer you get to the network edge. Its still terribly important for IP Phones, teleconferencing, and other applications where near perfect 'real-time' no-latency delivery is necessary, but I don't see much use beyond applications like that.
'Next Header' replaces anything resembling a protocol field. It is used so that rather than track a protocol following a specific format and size, a packet can just contains what the next header is. When a device needs that next layer, it just jumps down the packet. More than one header might exist in the packet, and we'll talk about some of the ramifications of this later.
There are two other things one should notice. Number one, the lack of an IP checksum in v6, which is almost a direct result of the stability of networks and the acknowledgment that layers above IPv6 often have checksumming routines in them. Additionally, basic IPv6 packets, are a uniform size. This drastically speeds up processing of packets in routers. Designers realized networks are getting larger, both in bandwidth and in users, and making the protocols as fast as efficient as possible was a good idea.
The goal here was efficiency. Routers were limited in CPU, memory, and bandwidth available. It was critical to wring out as much in IPv6 as possible. IPv6 packets are larger and routers need all they can get to push packets around. This is as much true today as it was then, maybe even more so since large companies push several gigs a second, which is a far cry from 1998.
Please note, I didn't use the word 'security' once in that post. I didn't need to, there is no more security there than in IPv4.