Based on the way you’re worded your question, you obviously know how broad any answer has to be when talking about ‘Roman citizens’ in general. The Roman Empire in the third and fourth century were large places, and we cannot assume everyone felt the same about what was going on. For example, a citizen living in Constantine’s new Christian city (Constantinople) would likely have led a better life than someone living in a town on a bank of the Rhine.

So let’s start with how people felt right at the beginning of Diocletian’s era, in a broad sense. The Empire had really lost all ability to defend its borders, barbarians seemed to be invading at an endless rate, and with continuous civil wars sapping men from the frontiers it really didn’t look like it was a situation that was going to get any better. If you were a citizen actually on the border (on the Rhine or Danube valleys), you would probably have to leave or accept looting/raiding as a part of life. It was so bad that peasants actually came together to form ‘bagaudae’ (peasant armies) just to protect their land.

The Empire at this time was a place where one could not be sure whether the most recently proclaimed general-emperor would be any more or less successful than the next. Aurelian (AD 270-275) is generally treated very well, but he only reigned for five years. Diocletian might have been viewed very similarly, especially considering the murky circumstances surrounding his ascension, at least for the first few years of his reign. It is possible that even by AD 300 Diocletian that there was still an expectation he would be overthrown.

By Diocletian’s reign, the coinage had been debased (reducing the quality of the coinage by using cheaper metals - ancient inflation) to the point where money had become practically useless and a system of basic item trading took over (which was even used to pay taxes due to the absence of useful coins). Local officials in towns and cities (curiales, decuriones, curators) had to be forced to do their job because no one could be bothered to do it anymore (it was unpaid and money was short for the time being), so civic life everywhere had begun to deteriorate.

Overall, it seems like this was a gloomy time, one where your grandparents could have told you that the situation had been pretty dire for a long time (it was the third-century crisis, after all). It is hard to imagine anyone would have been oblivious to this, and any sustained improvement was likely to be felt.

By the end of Constantine’s reign, the barbarian invasions had been subdued (temporarily), coinage was reformed and new mints had been built all over the place, and (despite the chaotic ‘civil wars of the Tetrarchy’ which followed Diocletian’s abdication) there had been some pretty long-reigning emperors, especially Constantine. The radical changes Diocletian introduced followed by the stability of Constantine’s long rule certainly did a lot of good and fixed many of the crippling problems that had plagued the Empire for a century. You would imagine that this would seem like a pretty nice place to live, a peaceful and prosperous Empire full of the new ideas of Christianity. However, this was not necessarily the case. There is a pretty fierce debate (like, so fierce that I’m not going to go too deep into it) about whether the Empire had begun to properly decline by this point (to the extent that collapse was inevitable), and there are reasons to think this. Constantine’s sons fought vicious wars against each other (and other usurpers) while they ruled, and by AD 378 the Empire was in such a poor state again that it experienced one of the greatest defeats in Roman history (Adrianople). By 378, it it fairly certain that the fall of the Empire was inevitable (not to the actual citizens of the time - Rome was eternal, remember - but from the historian’s eyes), so can we really say that life under Diocletian and Constantine were peaceful and prosperous times? Probably not. Can we say that an improvement was felt (or at least a route to improvement), it is hard to say. Diocletian’s abdication sparked a series of civil wars which only ended with Constantine and Licinius (Constantine’s co emperor whom he eventually fought and defeated) in control. Constantine’s reign had its own problems; Christianity proved to be a difficult world to navigate, and Constantine ended up exacerbating divisions within the Church, namely the Donatist schism. Writers like Ammianus Marcellinus showed the period following Constantine’s reign to be a difficult one, and it doesn’t look like this was incredibly different from the periods preceding it. Bear in mind, the only people who had not seen civil conflict in over a century were those who were born just after Constantine became sole emperor, and even then they would only have been thirty when the disastrous battle of Adrianople happened. Based on that it is hard to imagine anyone really seeing a major improvement at the ground level. Emperors like Diocletian and Constantine might have brought short periods of peace, but it never lasted, and problems still existed which were part of a crumbling system of debt and an ever enlarging number of enemies.

To answer your question, you must think about how people would have thought their life was compared to their parents and grandparents and, as I have mentioned, the only generation who would have had any chance as a good life were those living under Constantine, but they still would have experienced either the effects of the violent civil wars of the Tetrarchy, or the wars of Constantine’s sons and the battle of Adrianople (which was so horrendous that one half of the entire Roman army was just gone afteraard). So no, I do not believe people could have considered their era a vast improvement from the preceding crises, but you may examine the evidence yourself and disagree, because that is my interpretation of the evidence I have laid out.