From 1943 FW documents for Ta152B/C proposals included the C3/4/5 to be armed with 3x MK103 (docs reproduced by sqn signal iirc), two would be synchronised for ground attack, one through the hub and two defensive MG151/20 in the cowl. One prototype was built, the 190V65 but the wing root guns couldn't be synchronised, so by Oct44 the armament for the 152C3, which now encompassed all the roles of the Ta-152B/C close support variants (there was originally going to be about four subtypes with differen equipment/engines, but they cut it back to one multirole using the daimler), so at this time...
...in Die Varianten der Ta152C reproduced in Dietmar Hermann's book (dated Mar45), for actual production listings (tooling was being geared up from March), the armament for the C3 had been changed to 4x MG151 chambered for 15mm due to complementary ballistics with the MK103m motorgun. This would be because 3x MK103 was unavailable for technical reasons and it was the best second choice. It was the final armament decision for the C3.
Rechlin found their ballistics with normal AP/APT type shells surprisingly complementary up to about 600 metres varied calibre grouping with the same flight time of 1sec to 700 metres, meaning a volley from the mixed calibres is likely to strike the same target without too much trouble in a typical ground attack pass...or shooting a bomber's cockpit with pinpoint accuracy from over half a km away.
With an MK108/MG131 combination for example, you only get groupings at 150m and again at 350-450m (depending on calibration of vertical convergence set on the ground, usually 350m), once when the heavier shells passed up through the flight path of the lighter shells, again when they passed back down through them. So you could only hit with all your guns at either 150m target range, or usually 350m target range, and either side of those ranges means you hit with one gun type or another. Not both.
This is the reason for the consideration, especially for a heavy ground attack fighter, who needs at least 500m range of complementary ballistics on all his guns if he wants to hit average targets with all his guns. You walk your fire up transport columns with each target getting further away as you run out of airspace under the wings, the more lethal range you've got for each and every pass you have to make the better.
The MG151/20 and MG131 combination for fighters for example have complementary ballistics out to about 400 metres with a good grouping, and the same 1sec flight time to 500 metres. It means they don't actually group well any further out than a well set MK108 vertical convergence, but all the way out to the maximum set lethal range for convergence firing you hit with all your guns and if you walk them a bit you can still hit with all guns out to the 1sec flight time range easy enough. So you get more adaptability with the 151-2cm/13mm combination than you get with 108-3cm/13mm. You don't actually get a greater lethal range per se, just the MK108 lobs its shells in a great arc under to get to 350m true, the 2cm goes much flatter.
What you really don't want is two gun types that have different flying times as well as different "throws" as you've pretty much no chance of hitting the same target with all the guns unless you do something like they do with the MK108 in the Messer, you have two ballistic intersections between the guns tooled with a vertical convergence, you have to be pretty much exactly at that range to fire and get all of them on target. You can do that air-air but it's seriously not ideal for air-ground because you need to walk your fire around target concentrations just to hit something in the first place, and the plane might not want to do exactly what you want in this 2D environment where it will in a 3D environment because the target is flying relative to you, not moving relative to the gound.
The MG151 15mm ammunition was stockpiled already. The rechambering of the 151 for 2cm was a little sudden and unexpected from my impressions although a real expert like Tony Williams would know the history of the weapon more than me. The BoB hadn't been lost when production was tooled and the emphasis was on a dual purpose motorgun with tungsten option, in 1941 the emphasis changed and included pilot protest, so that now they wanted a single purpose air-air gun with m-geschoss option instead.
So the 15mm has tungsten rounds available but no m-geschoss. The 2cm version has no tungsten but has m-geschoss option.
So it is a matter of both complementary ballistics and readily available ammunition, because you arm planes for the role you want them to do. And the 15mm was meant for dual purpose, that is a ground attack (light-AP) function. It fires flat, true for a long way and goes though an engine block. The 2cm has a bigger punch but sacrifices some of these qualities. ROF is pretty much identical between the calibres.