In the first place I think we should recognize that there are two assumptions here. The first is that armies in the late Republic were more loyal to individuals, the second is that armies were supposed to be loyal to the senate. There's actually a third, that something changed, but I'd consider that subordinate to the first two. In point of fact I don't think either of those assumptions is true.

The second, that Roman armies were supposed to be loyal to the senate, can easily be disproved. There's this perception outside of scholarship, based mostly on the work of Ronald Syme early in the 20th century, and his predecessors in the Victorian Period, that the Roman state consisted solely of the senate. As Syme put it, "In all ages, whatever the form and name of government, be it monarchy, republic, or democracy, an oligarchy lurks behind the façade." That statement must be considered to hold if the resulting argument, that we can safely dispense with Polybius' famous description of the ideological foundations of the Republic, is to hold. Following Syme, and supported by a reliance on prosopography, the dominant view in one form or another was that of an aristocracy--following Gelzer's monumental Roman Nobility, specifically the nobiles, those individuals with consular ancestors--controlling voting through networks of clients, which might extend throughout Italy (as Badian's Foreign Clientelae showed). In this view, although Polybius describes a Republic in which the citizen assemblies, which alone were responsible for all legislation and magisterial elections, the senate, and the consuls specifically share power and have legal means by which no single unit can gain power over the others, we should imagine the Republic as firmly under the control of a small group within the senate. Since Fergus Millar's monumental article, "The Political Character of the Classical Roman Republic, 200-151 B.C.," this has been called into serious question and, in the strict form involving clients and all that, universally discarded. Millar pointed out that Roman politicians spent a great deal of time speaking to the people in contiones and at other addresses, and that in almost every single political discourse of the Republic we find repeatedly the testimony that it's the populus who's in charge. Foreign powers frequently present addresses and inscriptions to the Roman senate, but as Polybius points out the senate dealt with foreign embassies and therefore was, to the foreign eye, the face of Roman politics. This is now probably the largest question of the study of the late Republic, the question of how "democratic" (or, conversely, how "oligarchic") the Republic was. It is far too long and involved for reddit's purposes--the two current positions are probably best exemplified by Mouritsen's Plebs and Politics and Morstein-Marx's Mass Oratory (backed up by Yakobsen's Elections and Electioneering, for a more targeted study). Let it suffice to say that nobody currently equates the Republic with "the senate." Even Mouritsen, who argues that "real" political power rested in the hands of a relatively small number of individuals, must concede the importance of the citizen body in the ideological rhetoric of the Republic, and gets around this by arguing that the populus Romanus was generally unconcerned with politics. Ideologically, though, the Roman armies were not representatives of the senate, but of the Roman people. This is abundantly clear if we consult the texts. And indeed even in the mechanism of raising an army we see that the ideological weight is on the populus which made up the army, not the senate which had little to do with the citizen assemblies that elected magistrates and passed laws. Legions were raised by military tribunes, some of whom were selected by the senate but which nevertheless represented and were elected by the voting tribes. The Roman army elected its own leaders, the consuls, through the comitia centuriata, explicitly thought of as the Roman people in their guise both as electorate and army. And, as we are repeatedly told in our sources, only the Roman people could grant and remove the magistracies that allowed individuals to command them.

These last few points are pertinent, because there's also a separate controversy, albeit one with a much clearer general consensus, regarding the "loyalty" of late Republican armies. The so-called "Marian Reforms," and particularly the abolition of the property requirement which was thought to be so influential on the character and morality of the armies, have pretty much no evidence to back them up. The abolition of the property requirement is conjectured from a remark in Sallust that describes Marius enrolling unlanded volunteers. But this is during a manpower crisis, and there's nothing in Sallust to suggest that this henceforth was any less unusual than the enrollment of slaves in the army after it had been done for the first time in 215--indeed, all our evidence for the composition and enlistment of armies even into the Principate suggests that there was no great change in the enlistment of Roman soldiers. There is a line in Appian, describing Sulla's troops' lust for the plunder of the east, that scholars in the early 20th century took as indicative of a "mercenary" army that was only out to enrich itself, and would follow any leader that did so. But as Keaveney has pointed out desire for plunder as the motivating factor in pretty much all military actions pops up in our texts all the time before this, and the soldiers stationed at Nola in 88 had every reason to worry that they would get shafted--in Marius' first consulship he had recruited a new levy to go to Numidia, and that army had received all the glory and plunder, rather than the one that was already there. The troops at Nola had been laying siege to an Italian city with little reward for themselves, and they were threatened with suddenly getting the shaft. Moreover, this "mercenary" desire for plunder does not seem to feature in any of our other descriptions of civil war. Cinna's troops, Keaveney pointed out, could not possibly have been motivated by plunder in 87 (and the texts do not say they were), and none of our texts say that Catiline's troops or Caesar's turned against the city for plunder. In fact, the cases of Sulla and Cinna are indicative of the sort of rhetoric that is actually used of such civil wars. To save time and space, I've written on the subject here. Cinna (whose troops were not even his own!) and Sulla did not appeal to their troops' loyalty to themselves or to their troops' desire for material gain (even land settlements is not a good explanation, as there are only like four cases of veteran settlements before 49). Instead the rhetoric used was rhetoric directed at the army as representatives of the populus Romanus, imploring them to reestablish the normal constitutional procedures of the Republican state, which it was argued (and the soldiers apparently bought) was under attack. This pattern repeats itself again in 49. If this is the case, as our sources appear unanimously to say it is, then we cannot really talk about soldiers having loyalty to individuals rather than the Republic, can we? Since the very ideological basis on which the army's action of initiating civil war (or not initiating it, in Caesar's case, since Caesar had war declared on him, not vice versa) rested was one of the populus Romanus exercising its powers according to the laws of the Republic and reestablishing the legitimate government by very definition the armies of the civil wars do not appear to have thought of themselves as agents of individuals at all.