(which on a side note puzzles me as I would expect a CPU released 4 years later to be a lot more powerful).
You are expecting something that just isn't (currently) true. CPUs have really plateaued over the last several years, so each generation is an incremental move toward better efficiency rather than a leap forward in raw computational power and clock speed.
Also "powerful" is a subjective term, and your also comparing an ultra-low voltage dual core ("U") to a quad core for mobile ("QM"), so it's hard to know what you're expecting exactly...
What improvements have there been between generations?
To find out some basics let's consult Intel's ARK:
Major advancement - die size:
Which is a major contributor (along with only having half as many cores) for this improvement:
This lower TDP and tighter lithography lends to things like improved battery life.
Other than that, most still looks equal right?
Now consider why they changed architectures, and what new designs may add.
A non-specific, hypothetical example would be improvements in certain calculations. They can (and do) implement new features that do certain (sets of) calculations much more efficiently. So, for example, they can now do calculations X, Y, or Z in one clock cycle instead of 3, therefor tripling the performance of those calculations, all without changing clock speed, or enlarging caches, or widening memory bandwidth. If you use those certain calculations a lot, you're going to notice a massive speed improvement.
If I want to do tasks in the browser (Gmail, Google Calendar, Youtube, Gogle Drive...), which of Core i7-2670QM or Core i7-5500U is more powerful?
It will probably make little to no noticeable difference with that kind of usage.
To really know the difference, you need to do benchmarks and compare.
According to 3DMark's Benchmark comparison (higher is better):
The 5500U scored a ~40% higher score, with only half as many cores, while using ~1/3 the electricity.
This tells me that the 5500U is considerably more "powerful" (at least in this one benchmark. :) ).
Once you start looking at multi-threaded benchmarks, a quad-core (that close in age and architecture) will often (if not always) outperform the dual core, for obvious reason.
At that point you should probably be looking at comparing to a 5th generation Quad Core (ie: the i7-57X0 and i7-58X0 processors @ ~45W TDP), and do further benchmarks to get a more apples-to-apples comparison.
Core i7-2700QM
just because its several gpu generations newer. So does that count as being more powerful?HD Graphics 5500
considering theHD Graphics 3000
was considered to be complete trash by most people ( in other words bargain bin performance ).