Yes, better multitasking if you want to do anything in the background minimised quickly, smoother system transitions, less framerate hits due to any background processes, voip/any streaming you may do, once again background resources available and more cores available to everything.
Honestly... I never regretted going I7-2700K over 2500K as over the years, the threads have helped keep my current system responsive and more fluid than it would have been, and helped keep minimum framerate up (OK a substantial OC has also helped!). This is more of the same, but this time around, people will have the choice of say a lower tier, moderately clocked Intel chip, versus a comparable AMD chip generally offering more cores and performance overall. AMD will be looking to get the balance of cores/threads/clockspeed correct to stay competive across the board, and I suspect except for the most highly clocked comparatives, they will be pretty competitive in single core performance across the range, whilst trouncing them when it comes to multicore...and therefore system fluidity...across the board at a given price point.
Intel i3 price point - 2c, maybe hyperthreaded, will be against genuine AMD quadcore with SMT bleeding in higher up the product stack
Intel i5 price point - 4c, maybe hyperthreaded, will be against genuine 4c8t and even 6c parts
Intel i7 price point - 4c8t, will be against AMD 6c/12th and 8c16th parts.
Providing clocks and pricing is competitive, thats a big deal, even for a pure gamer, as it means the system will last longer before it needs changed.
I can guarantee you if I'd bought a 2500k I'd have wanted to have changed it by now as my workload and games are demanding more.
Just to copy for reference one of the older tables:
Convert those prices to pounds and then consider based on what we've seen yesterday, the clocks may actually be higher than originally specced on the R5/R3 parts. 1600X is going to be 3.6GHz/4GHz boost for example, AMD may be releasing later so they can spend more time tweaking clocks before they release.
Compare the current Intel price stack. Those R3 will absolutely annihilate Intel's i3s for the money etc given reasonable single core IPC.