Nautilus the default file browser has the feature of mounting remote files.

Go to File Menu > Connect to Server..

Other than that filezilla and gftp support sftp.

Since you are familiar with Winscp on Windows, I suggest that you try filezilla

FileZilla Client is a fast and reliable cross-platform FTP, FTPS and SFTP client with lots of useful features and an intuitive graphical user interface.

You can also install with the command line. Open terminal Ctrl+Alt+T and run following command:

sudo apt-get install filezilla

Or search on Filezilla in Ubuntu Software Center.

When you add a host, be sure to change from FTP to SFTP, and change the port number to ssh port 22 (or other custom ssh port if different)

Make the account type interactive.

Enjoy.

You could also use sshfs or rsync.

sshfs mounts your remote directory locally over ssh very similar to WinSCP and Nautilus.

The potential advantage of sshfs is that you can map users

sshfs -o idmap=server_user user@server:/directory ~/remote_directory

To automate the process, add an entry in fstab

sshfs#user@server:/directory /home/your_local_user/directory fuse idmap=user 0 0

See Ubuntu Wiki SSHFS

rsync will also sync files / directories and will work over ssh and has a graphical front end, grsync

See Ubuntu wiki rsync

Last you can edit remote files with vim (if you are interested)

vim scp://user@server//path_to/file_to_edit

You can still use winscp under wine. I am doing the same, and it works very good.

You want "scp". The original scp :-)

Oops, I spoke too soon... you have requirement of syncing as well. In that case, rsync.

However, scp is still good for scripts and automation.

Ubuntu:

Open Nautilus and type (in the link bar): sftp://user@server/

Kubuntu:

Open Konqueror and type (in the link bar): fish://user@server/

Xubuntu:

Open Thunar and type (in the link bar): sftp://user@server/

There are many different tools which would give a similar experience as winscp. I use filezilla for transferring files across ssh.

Nautilus as mentioned by @sagarchalise allows for connecting to server.

One of the things I use more often these days to access sftp is sshfs. I find it very convenient as it mounts the files as local file in the filesystem and transparently updates it on the remote server.

sshfs [email protected]:/path/to/remote/files /path/to/local/mountpoint/

It lets me use all my usual tools assuming these file are local files.

You can also try unison to help synchronize the two folders

A very nice and powerful program, built over the rsync protocol, is Unison.

It has a very nice interface, and the client is available for at least Linux (more or less all variants) and Windows. The basic behavior is very easy to grasp, with a graphic interface and easy configuration, and if you need to do more complex things, you can manually edit the configuration files and/or script it.

It has been my backup/mirroring/uploading utility in the last five year at least, and never saw a bug or missed a file.

You can install it with

 sudo apt-get install unison-gtk 

and for a smooth behavior, you should have configured a working connection with your endpoint (I normally use ssh connections).

I recommend PCManFM sudo apt-get install pcmanfm

Just another File Manager but features a mini GUI for connections (in main menu Go --> Connect to server) and there you go. You can bookmark your connections and you can just right click files and chose "open with...".