So it is very difficult to say with any certainty from photographs, so I will use assumptions. I asked about the location because, if early war the odds differ.
The .54 cal. has a better chance of being Southern, but if it were from say, Manassas, an early war site, then it’s 50-50. The Federal army did its best to try and standardize on .58 where it could, particularly in the East.
The typical .54 weapons would be M1841 and the Austrian Lorenz, both were bored out by Federal arsenals to some degree. The South did not have this opportunity on a large scale and as such was more concerned with getting arms to its troops.
The 2nd Maryland CS, for example had over 10,000 rounds of .54 issued just before Gettysburg. We know that they had M1841s and from piecing together, it is figured that two companies had these weapons and were used on the flanks. The balance of the 2nd had a mixture of Enfields and captured Springfields in .577 and .58 respectively.
Without being able to see the grooves closely on the .58, it appears to be what is called a Williams Regulation Bullet with square grooves. Again it is hard to tell the groove configuration from the photos. Williams Regulation would be Federal.
Your round ball has a better chance of being Southern, but again that is just playing the percentages and as with the .54 it would depend on early or late war location. Even then there were Federal regiments that retained their .69 smooth bores out of preference. Most combat is within 100 yds, buck and ball was devastating within that range, firing at closely packed formations. I believe I see dimples where the three buck would nestle against the larger round ball, but again not being able to hold it, who knows.
Nice bullets and as
@FedericoFCavada has stated, a start to a nice collection?