Whats the deal with these new lower clock speed CPUs on Laptops? Can they still run apps well?

Clock speed speed has been misleading for a long time now. Intel has had 3.2Ghz chips on the market since the P4 back in 2002/2003, and even at that time AMD's lower-clocked alternatives out-performed them. Unfortunately, there's not much to go on these days in terms of what the performance of a given chip really is without benchmarking.

But in the case of the AMD Neo family, the best comparison is to an Intel Atom processor used in the tiny netbooks. The Intel Atom is intended to give up some performance in exchange for better power use, a smaller chip size, and a lower price. In my experience, AMD's Neo alternative kept a little more performance (of course in exchange for power consumption). Some of the nicer Neo's perform as well as an older low-end Core 2 Duo, which, considering disk performance often matters than cpu these days, is still nothing to sneeze at. Pair that with one of the new low-power graphics chips from nVidia and you have a very portable and low-power system that still packs quite a wallop.

Its all about the architecture and bonus features.

Just like GPUs, CPUs have made it to a stage where looking at their specs you have no idea what their overall performance will be, the numbers on the box are fairly meaningless these days.

The Neo cpu is an AMD celeron analog.

The P6000 in your other example is a lower power core2 chip (25W vs 35W TDP), performance falls off as expected from the lower clock but you get better battery life in trade.

For intel's newer I3/5/7 mobile chips the base clocks of all the normal power ones are in the 2-2.5ghz range and are about 20% faster per clock than the core2's they're replacing. The i5/7 chips can also temporarily increase their speed by a few hundred mhz under heavy load.

The ultra low power chips are roughly half as fast but can boost even higher for short terms. They're also aimed as replacements for the ULV core 2's that ran in the 1-15ghz range. They're not intended for CPU intensive apps although for compiling turboboost can probably help a lot. Gaming less so because the high sustained loads will have the chips clock back down as they get hotter.

Intel doesn't currently have a direct replacement for the 25W TDP core2 chips like the P6000.