Your brain won't be roasted, that is bullcrap, there are enough frequencies in the air that this won't make a difference anyway.
Regarding microwaves, the only reason they are legal is because they incorporate a Faraday cage, no energy leaves the microwave.
The legal limit for EIRP (broadcast power with antenna gain) in Europe is actually 100 mW with a normal antenna, not only is the other adapter illegal (as could be the case with your current one), it will make your connection and ability to see networks worse.
How come? Simple:
Upping your broadcast power allows routers further away to hear you, but WiFi is a two-way connection and just because they can hear you, doesn't mean you can hear them.
Therefore it won't change anything, the routers you see in your area now are the only routers you will ever see, no matter if you use a 50 W or 0,1 mW link.
Why is this then? When showing available routers, all a WiFi adapter has to do is listen, it doesn't have to transmit anything untill it has to make a connection, so its broadcast power is utterly pointless.
As your current 200 mW adapter is already pushing the limits of legality, you won't see any improvements unless there are illegal routers you can see, but not connect to, that transmit at an even higher power.
Even then, someone with the know-how of setting up a high power AP will probably know how to secure it well too.
Why will it only be worse with the new adapter? Noise.
As you increase the power of a transmission, it induces noise.
The higher the power, the higher the noise, so the 3 W adapter would be able to connect to even fewer routers.
What can you do to improve your situation?
Look for receive sensivity on the adapter, you want this number to be as high as possible, this allows it to receive weaker signals from routers further out.
The best thing you can do is get an improved antenna, preferably directional for these long range connections.
There are many DIY projects using a pringles can, a wok (or large bowl covered in aluminium foil) or an old satellite dish.
Alternatively, you can get specially made WiFi dishes made to last outdoors, I've seen plenty with high gain and good quality around 20-30 euros.
If you attach one of those your adapter, you'll see much better results, for an even more stable connection, you could couple the antenna with a good router (if the routers around you operate on 802.11G, get the Buffalo WHR-HP-G54) and have it take care of the connection.
Regarding 802.11N, it has longer range and a higher speed throughput, but the router you are connecting to needs to be 802.11N or it will just make an 802.11G connection.
802.11G is still the most widespread, but if you know your neighbours have upgraded to 802.11N, there's a benefit to gain there.