Problem moving website to a new host

I had HostGator transfer my website from my previous site to HostGator.
The size of all of my files on the old host is 175.31MB (183,823,925). On the new host when I check the size of all the files it is 140.34MB (147,159,052).
Then is another test I downloaded the files to my computer from the old host and it shows (175.31MB). I thought it just has to have something to do with the file system on the new host so then I downloaded the files directly to my computer from the new host thinking it would then show up as 175.31MB but it shows up at 140.34MB. It definitely is missing some files. the old host is showing 11,000 files, the new host 8,848 files.
I'm not sure what's going on but I'm sure so me files must be missing so I haven't switched the DNS over to HostGator yet.
I am using Mac OS X and for an FTP program I'm using Transmit 3.6.6. I don't know if it's something to do with this program or even permissions stopping some files from uploading. I obviously have no problems downloading all the files from my old host to the computer but it seems something may be wrong with the upload.
I wondered if any of it could have to do with permissions. Also, when I reupload files that were downloaded from the old server would the permissions I modify (in files such as config.php for security reasons) still stay the same?
One more thing, I also have the Transfer mode since to Binary instead of ASCII or Auto in Transmit. I just want to make sure this is the right mode.
Thanks for assistance with this.
Unfortunately I took my website down Monday morning since that's the day I contacted HostGator to move it. Since it's almost been a week I'm desperate to get it back up for my customers. So far HostGator has been unable to help me with transferring the issue I'm having now and just needs to know what files are missing which I am unable to see. I just see this different in file numbers/size. Any idea what I could be doing wrong?

Compare the files/folders on each server with a full fileset to see if any files/folders are missing (or compare files on one server to the files on the other).

The difference may be extra files used by your previous host that the new host doesn't require.

Tina

Thank you for the help. Unfortunately my current FTP program does not make it easy to compare files and what's missing. I have heard of a program called Beyond Compare but it's only for Windows and Linux and I'm using Mac OS X. I'll try to find a similar program so I can do this for Mac.
I thought of maybe my new host not needing all files but I would still think the FTP program would copy all either way. I just don't want to assume it's working and run into problems with my website later and it's hard to know when I don't know what files are missing

Do you have more that 2000 Images?
If so unless the recursion is set to higher that 2000 you will only be able to see 1998 Images....

I just checked and the images directly has 3846 images, definitely more than 2000. I added it to the number showing on my server and it comes out around 10696 which is still just over 300 short of the 11000 so maybe something is still missing if this is the problem.
What do you mean by setting the recursion higher than 2000? Is this something I do in my ftp program for uploading or even in the cpanel on the new host?

Its something the Host has to set,
It limits the files that can be viewed to usually 2000

I'm thinking maybe another directory also has over 2000 items. I just finished writing HostGator asking them to raise my recursion to 10,000 if possible since I am adding a lot of images as more items are added.