It IS, and always WILL be more cost efficient to build your own pc.
This guarantees you know what you're getting, what it is exactly that you are getting
and allows you to steer clear of components/component setups that have proven to have 'problems'.
However if you do value mobility a lot looking at a laptop might not be a bad idea.
There are a lot of good quality laptops available at the moment, but laptops aren't really my forte so I can't help you with that. I know everything about desktops but
when it comes to laptops I am completely lost.
Regarding sites where you can buy pre-built 'customised' rigs (like dell.com or alienware or w/e) those rigs are usually quite expensive in the price/quality department not to mention they FORCE you to buy package deals (ie software/hardware you might not want / already have available such as windows or a mice or keyboard or w/e) so I'd suggest staying away from such things too.
RTS's are usually quite playable on 'older' rigs (granted you have to sacrifice some graphics) but the latest RTS will still run on a pc like your old one while the latest FPS might not.
I personally don't play any flight sims but I know enough to know they tend to be
quite resource intensive.. so if you really want to be able to play those I'd suggest getting atleast a dual core with a decent gfx card.
I don't quite understand what you mean by 'power user'?
multimedia playback doesn't require much resources and a low-end pc as long as it has a HD-capable gfx card and +-2gb ram should be able to play any movie/audio you want it to.
In case you are referring to audio/video editing now THAT is a completely different story. That stuff EATS resources and WILL ask for seconds. This sort of work (as far as I know) actually relies more on your CPU than your GPU (unless it's CUDA-capable software or something similar) and if that is what you want to do I'd suggest getting a quadcore cpu with as much GHZ as you can. Intel CPU's are more suited to audio/video editing than AMD's and AMD's are better suited to gaming (intel has a more GHZ is better policy while AMD prefers a larger bussize which favors gaming)
Also if this is your thing and you know which programs you (want to) use, check out if they are CUDA capable. if they are I STRONGLY recommend getting an NVIDIA GPU because it would greatly increase your raw processing power.
If you are into hacking and brute forcing / password guessing obviously more CPU is needed. This sort of activity usually doesn't require much ram or high busspeeds or anything.. just RAW and PURE CPU processing power. In this case again I would suggest getting an Intel quadcore cpu with as much GHZ as you can (I assume your tools have quad-core support)
a 1000 dollar budget will get you a sufficient laptop, a good pre-build pc or an awesome home-built setup. (with quality rising from 1st to 3rd choice).
If you have any other questions feel free to e-mail me at: firstname.lastname@example.org
and I'll be sure to try and help you in the best way I can