The strap hands down! There is just no question.. I once saw a guy traveling carrying a Keepall with a small Bisten and an Abbesses and seeing him putting them down on the ground before boarding and getting his tickets and passports, etc.just made me feel I made the right choice in getting the same thing, but with a strap! You will tend to load it up and carrying it by hand, it will hurt and become cumbersome!
I just picked up my Keepall 55 in Damier Ebene with the strap this morning. I'm glad I did, it's as everyone else has mentioned, it's better to have the option whether to use the strap or not.
I picked this bag as I'm heading overseas for a long weekend and I'm loathed to check anything in especially for short trips (the quicker I can exit the airport after an 11 hour flight the better my trip is going to be).
That being said, my next purchase will be a Keepall 45 black epi (mainly to use as a carry on for shorter 1-2 night stays) and I'll revisit the issue of whether to get a strap or not after my trip next weekend.
The bag can get really heavy when full. so it is good to sholder it, even if its only for a few minutes. I considered a mon mono, but the plus on top of the price is only worth it, without the strap. If you want to use it for travelling, take the strap.
Get one with the strap. I have a Keepall 45 without, and don't use it much because I wish it had a strap. Being Monogram, I don't ever want it to touch the ground, or hold onto the handles all the time.