IMO, a great deal. AIUI, Stalin was extremely paranoid about being sucked into war by British provocations. He insisted that Soviet forces at the frontier be in a state of non-readiness, so that even if some accidental bang went off, there would be no chance of escalation to actual combat.
The result was that BARBAROSSA began with a colossal sucker punch. A small but significant part of Soviet forces were hit while unable to fight and destroyed immediately (battalions and regiments). That created gaps in the Soviet front which German forces pushed through to strike and overrun rear-echelon troops (divisional and corps HQs, depots, artillery). The "line" troops" were hit on flanks and rear and were routed or encircled. The failures cascaded and snowballed until the entire forward echelon of the Soviet forces in the west were destroyed. Trying to contain the disaster, the Soviets threw any forces they had in the path of the advancing Germans to buy time, including technical units, training formations. Most of these were also destroyed, with longer-term consequences. The collapse in the center allowed the Germans to stage the Kiev encirclement.
By fall 1941, the Soviets had lost not only a huge number of troops, they had lost a lot of the army's technical and training personnel, which crippled the process of raising and training fresh troops. Large numbers of men with poor or partial training were flung into battle as the Germans pushed toward Moscow and inflicted additional massive losses. Finally the Germans became exhausted and winter set in.
If Stalin instead decides the threat is real, then Soviet forces will be in a much better state of readiness. The Germans will still win the battles in the frontier areas. Soviet tanks are still crap, and the rapid expansion of Soviet forces still diluted the officer corps with under-trained neophytes.
But there will be fewer walkovers and more slugfests where the Germans use up ammunition and fuel, and suffer damage to vehicles. In consequence, there will be fewer deep breakthroughs and encirclements. IOW, a "reverse cascade".
Another important point not widely known is that British intelligence had lots of ULTRA information about the German forces deploying for the attack - like, a complete TO&E. They presented this information to representatives of STAVKA in mid-July. Stalin ordered STAVKA to ignore it.
If Stalin thinks Germany is going to attack, then he will allow STAVKA to accept and act on the British information. Soviet deployments and reactions will be far better thought out if they know where all the Germans are coming from.
I've never found an authoritative statement of BARBAROSSA casualties broken down by month, which I want to isolate the opening stage (22 June-August) from the follow-up stage (September-October) and the final stage (November-December 4). My WAG is 6M permanent Soviet losses for the whole period, to 500K Axis (German, Romanian, and Finnish) of which half came in the last stage.
My WAG for BARBAROSSA against a fully prepared and alerted USSR is 3M Soviet permanent losses to 1M Axis. This is still a colossal Axis victory - but not super-colossal, as in OTL.