Will AMD processor run everything like and Intel chip?

No, AMD chips operate in their own dimension, in an imaginary space between existence and void.

AMD and Intel are 100% instruction compatible with each other except for acceleration instruction sets, e.g SSE SSE2 MMX etc etc.

If it was me, go for an Intel i3 or i5 socket 1156, as they are far superior and cost very little more.

'far superior'? What world to you live in? Better, yes, but only in terms of benchmarking, day to day use you cant tell the difference.

Better than what? The i3 is beaten easily by the athlon 2 x4 in everything except gaming.

If you are spending under $200 on a chip AMD is the way to go. The one chip having a higher frequency than another doesn’t exactly may if faster; their design is different which make them perform different. Look up the bench marks of the chips you are looking at and then look at the programs that you use to see what performs best. The people who bring up ‘far superior’ and i5 have not read all of the forms here for good information. The i5 and PII 965 trade blows with i5 wining a few more by slight margins and overall costing about $50 more.

Guys, my main concern is that I heard AMDs are 64 bit while intels are 32 and if I dont use 64 it os andn software on amd it will be slow?

You heard wrong, Intel chips are 64 bit as well. Both companies have a 32-bit compatibility mode, and things run just fine that way.

No it's fine. You don't need a 64 bit OS to use a 64 bit cpu. Also, intels are 64-bit too, all recent cpu's are.

Thanks to everyone for advice and helping out. I've decided to go with AMD.