At first glance Krav Maga and Systema seem to be very similar in that they are both very unconventional, no-rules, practical self-defence, martial arts (although Krav isn't technically a martial art) which are no holds barred and generally formless.
Krav Maga is basically a very raw, dangerous situation survival system (including avoidance and escape) which builds upon your natural instincts and taught in a very short space of time. Therefore it is highly stress tested. It relies on the fact that fear will set in in order to use your natural responses and turn them into functional movements to your advantage. It relies heavily on shock and awe in that defence and attack should be simultaneous where possible to capitalise on the opponents shock value.
Systema is -in many ways- the exact opposite, it is a system which teaches over a much longer period of time how to control your fear/anger/pity and teaches relaxation (through breathing/stretching) in stressful situations so that attacks on your person are less effective, better recovered from and the pressure points, levers and momentum of attackers can be manipulated to your advantage using the clarity of mind gained from your training.
So in effect Krav Maga is taught fast and turns your weaknesses into strengths so your defence/attack becomes like a reflex just when you need it while Systema is a methodology that needs to be learned and seeks to remove you of those weaknesses so that your defense/attacks can be more effective.
Another martial art, similar and somewhere between these is the Keysi Fighting Method (KFM) -developed for street fighting- but that has some actual forms that have to be learned such as the very distinctive 'Pensador' that the Christian Bale Batman uses ;).
KFM is alot more like Krav Maga but it makes heavy use of the 'Pensador' guard (much like the 'Rhino' Krav pose) and concentrates a much larger chunk of it's time to dealing with multiple opponents and ground based fighting as it was developed for street fighting and this is where they tend to end up. It doesn't deal with survival (avoidance and get away) as much as Krav However. There are also no weapons.