Some basic Questions

1. with windows vista and windows 7, the os can make use of many cores and threads just
doing basic windows stuff. This usually results in faster system response. It may also depend
on how windows is scheduling tasks on real cores and virtual cores. If your desktop i3 is not
a low power model at 2.5 or 2.6 ghz but a normal power one at 3.1, 3.3 or 3.4ghz, it may be
running at a higher clockspeed than that low power i7 quad. your power saving i7 quad has
a default base clock of 2.1ghz, but can run at higher turbo speeds depending on how many
cores are in use. If it is 3 or 4 cores, the max is 2.8ghz. if it is 2 cores, it is 3ghz. if it is one
core, it is 3.1ghz. Since your i3 is always at one speed(not counting system idle), it may be
fully loaded. however, if the os is loading the i7's cores one at a time so they are all working
before using virtual cores(hyperthreading), it may be throttling at 2.8ghz or 300 to 600 mhz
slower than an i3 at 3.1 to 3.4ghz. that is the best guess i can think of.

2. Mem speed Not a big difference, no. probably not enough to notice, anyway.

3.4GB should be ok(depending on the kind of work loads you want to subject your i7 to).
I am wondering about the os. flipcart says it is windows 7 home premium, but does not
specify if it is 32 bit or 64 bit. one would think that a system with 4 gigs of ram (up to 8),
and video card with 2gigs of its own ram would have windows 64 bit. If for some strange reason
it has windows 32bit, that is a hard limit on the amount of memory that can be addressed in
the system(4GB) and takes away from system ram based on the amount of graphics ram and
other things. If you are running windows 32 bit, you are likely using less than 2GB of you
system ram. If it is windows home premium 64bit then it can theoretically have a up to
16GB of system ram(a limit set by microsoft versus 128GB of ram on pricier versions of
win 7 than the home version) but also allocate possibly any amount of dedicated graphics
ram above and beyond that.

4.It might be possible that the hm76 chipset is limited to running ram at 1333 max. but not
sure on that. even so, it wouldn't make that big of a difference to overall performance.

5.the i5 might possibly be better for day to day/games, but not heavy workloads.

6. can't tell whether a hdd swap is very feasible or not in your case.

Going along with that, what speed was you hdd in the desktop? your laptop hdd is only
a 5400rpm model(i guess that is standard on a laptop versus 7200 rpm on a desktop).
Your hdd performance could be a bottleneck to the system you are not used to.

Thats all I can think of that might be causing you to feel things are slower.