Will nVidia 7300 GT 1 GB be faster than AMD HD 2600 XT 256 MB or nVidia 7600GT 256 MB??
NO. 7300 GT is simply not fast enough to make use of that 1GB video memory. 7600GT and HD 2600 XT are much faster despite having only 256 MB of video memory. Like I told you above, the only way to judge performance of a graphic card is by looking at FPS numbers delivered by them in games. For this, you need to read reviews and research yourself.
(Note: The cards mentioned in this question are end-of-line and very old. Don't think these are good cards in 2011)
Fun fact about Laptop GPUs: If you are being happy because your Rs. 50,000 laptop has 1 GB or 2 GB video memory, no need to be happy about. AMD HD 6770M which is the fastest mobile graphic card in laptops costing around Rs. 50,000 in the Indian market, it performs around the level of HD 5670 (dekstop). It is hardly helped by video memory above 512 MB. What about Intel HD graphics? Intel GPUs suck as far as graphics are concerned. I hope you got your answer.
Will AMD HD 5670 1GB GDDR3 be faster than AMD HD 5670 512 MB GDDR5?
GDDR3 and GDDR5 are memory types. GDDR5 is faster than GDDR3. So, it is better to get AMD HD 5670 512 MB GDDR5. 5670 isn't fast enough to utlize 1GB memory anyways.
These days all high-end graphic cards use GDDR5. GDDR3 is mainly found in low end graphic cards. Many years ago, the low-end graphic cards used DDR2 memory.