First, I'd suggest making a plan for deciding what data is going where. A simple starting point is put all your media (particularly videos) on the hard drive, since it often accounts for the bulk of the data and benefits less from the speed of the SSD.
Secondly, you can customize what data Migration assistant brings over. Have it transfer your apps and settings, and maybe the basics from your home directory, then once you've got your system up and running you can transfer the rest either by running Migration Assistant again, or manually via Target Disk mode.
Another option, if you have a bunch of data (enough to get you under the 256GB barrier) that you know you're going to be putting on the HD, is to transfer it manually first (or to a backup drive), then delete it and run Migration Assistant without any exclusions.
Besides the obvious issue of you having too much information to load onto the SSD, I've done this basic procedure in the past. However, it's much easier now using Time Machine, but you have a few options:
Time Machine
If you don't currently have a backup that can hold all your data, do yourself a favor and pick up a drive that can. Time Machine should be built into the OS you're currently running.
Do the backup. For 400 GB, you probably want to set it up before you go to sleep and let it run overnight. Once it's complete, unmount the drive and unplug it from the computer. Go through with the drive install and then install Lion. When the computer reboots, before you start to work with the setup assistant, plug in the new drive. At some point it will prompt you for a location from which to migrate data. Select your backup. Let it run for a while and when you get back, it will contain all the data you backed up, in a usable form. This is my current favorite method for cloning user workstations.
Super Duper
If you can't get an external backup, you can use SuperDuper to create a full-system backup from the active system disk. You'll have the ability to trim the data to the size of the disk to which you're copying in the interface. This route is a little more technical and requires a bit more time hands-on.
File Copy
I wouldn't recommend copying a user folder for a logged-in user due to open preferences files. You'll get all kinds of "File In Use" errors and it will probably exit the copy prematurely. Instead (if you're dead-set on using this method - which I advise against) create a second admin user and copy the folder over into a temporary location before staging it into the actual /Users/ location. You'll also need to make sure the permissions for the entire folder are set so that the user whose home you are copying can actually access and write to their files. To do this, you can use the Finder's Get Info on the folder and then add the user to have full permissions. Once it's staged into the /Users/ folder, you can log back in to the main user and delete the secondary admin. You may have permissions issues in the future using this method.
All that said, it's totally worth it to get an external to back up to for Time Machine to clone your new SSD from.
Best Answer
In the past, I have just swapped the drives in the two machines, and everything just worked fine.
Take the SSD from the 13" MBP and put it in the 15" MBP.
In the unlikely event that there are any problems, you can always swap the drives back.
EDIT: You might want to boot into recovery mode, and do a 'Verify Disk' in the Disk Utility, to make sure that everything is fine. As suggested in a comment above, consider a PRAM reset and an SMC reset, to make sure everything is on the same page.