Cisco Catalyst upgrade from 3550 to 3750

Yes, most of it will copy over.  The only thing you'll need to change is the interface naming/numbering.

The config will be virtually the same, but there will be some syntax difference between the two.  I'd start out with the config from the 3550 and add it in line by line to the 3750.  Some command lines may be different since it's newer hardware and newer code.

In short, no, you won't be able to copy the config in and have everything work 100%  Trying it won't hurt anything though, you could just erase the config and redo it..

You suggest to configure it manually , instead of copy startup-config to tftp server?

You can copy the config from tftp and try it, the worst thing that will happen is that some of it won't work (which is likely).  If it were me, I would probably configure it manually.  It's not very difficult and shouldn't take long.

The interfaces are the only things that are going to get you.  You can copy the rest of the config (layer3 interfaces, etc...) but configure the interfaces manually.  The interface range command can speed things up, for example:

int range g0/1 - 20
switchport mode access
switchport access vlan 10
spanning-tree portfast

The above assigns ports g0/1 through g0/20 to VLAN 10, configures them for static access mode and puts them in STP portfast mode.

Thanks