Don't have experience with the SE, only the other one without a screen.
I think they are largely the same inside (receivers, antennae), might be some differences, but here is my feedback.
It is not clear when the messages are sent. They may appear to have been sent, but we have heard stories of messages "queued" in the unit. If you turn the unit off, then on again the next day, or even a week or a month later, the message could be sent at that time. The software is just not clear on this. The SE may tell you but the smaller unit does not.
There can be a log delay between when a message is sent and when it is received. We have tested message sending and receiving while on the radio with our groups. The group will say "we have sent the message" and we will wait 20 minutes before receiving it. The reverse is true as well -- the members in the field will wait for a long time for a message to get through. The smaller unit without a screen does not indicate satellite coverage. It might be as simple as this, but we tested in an area with a good view of the southern sky.
You cannot treat it like SMS, the messages can be delayed significantly.
The other thing we have noticed while using the GPS for tracking field teams is that when you compare the position with that recorded by a regular wilderness GPS unit, the regular GPS is more accurate. For the purposes of rescuing someone, it is just fine, but the company indicates through it's software that they consider it good enough for navigation. Probably OK most of the time but I would use a regular GPS if you have it. I do not have enough information on this.
If someone has a InReach SE and is willing to do the work I would love to compare the accuracy to other devices. I put together this web site to do exactly that: http://gpserror.azurewebsites.net/