A few things
Hmm. The macbook I have now (2009) has a 2.26ghz core 2 duo and 4G RAM, and it struuuuuuggles with those apps. My activity monitor tells me that I'm pretty close to using the whole 4G, but does the processor speed have nothing to do with it? For example, when I'm using around 3G of RAM it's still painfully slow to open a new to type, highlight, open a file etc. (The base MBA comes with 1.6ghz i5 and 4G RAM)
Thanks!
Firstly if you have updated to mavericks or yosemite, they use all of your RAM as much as possible and the only relevant stat in activity monitor is the memory pressure graph if it stays green then you have more than enough ram for your workload.
Secondly that sounds like either a full HDD slowing you down or an old HDD starting to fail. It may also just need a disk repair to be run in disk utility to give it a new lease of life. Unfortunately there is never just one possible reason for a slow computer and likewise many fixes possible.
Of course a new computer will fix these issues and 6 years is a good innings for any laptop.
So to your understanding of the differences between the laptops is where you are struggling.
Your old laptop has a penryn cpu it is not that powerful despite it's relatively speedy ghz score. The 1.6 ghz i5 in the current air benchmarks much better than the old core duo between 30% and 120% better depending on the benchmark!!
The SSD makes all the difference for snappy fast computer use and even just sticking one in your old macbook would make it feel much faster at everything. This will make opening apps, windows and moving between desktops a joy.
RAM is difficult to say if you have enough more won't make your computer faster, although it may run a bit smoother and easier.
Basically any of the current MacBooks will be a massive step up. I doubt you need a 15 inch one and if bang for your buck is what you want the 13 inch Pro is a better deal than the air once you set your ssd and ram levels the same.
I wouldn't worry too much about processor upgrade I'd just get one with the 512gb SSD so you have plenty of storage space and a good processor in the 2.9gHz i5 (the i7 is still dual core and is only about 5-6% faster is you are maxing out it's speed it's just not worth the cash for most people).