It’s not possible to answer such questions definitively because the nature of the disease burden has changed significantly and is not directly comparable to the past.

Large scale demographic trends such as life expectancy show a dramatic increase in recent years. While a large part of this is simply due to the reduction of infant mortality, there’s also a relative increase in the proportion of people who reach old age, 60-80 years.

On one hand you can see this as a reduction in diseases (mostly infectious diseases) allowing people to live longer. On the other hand, those who live past 60 have their own diseases to contend with, including heart diseases, cancer, osteoarthritis, etc. The incidence of diseases causing early deaths has decreased, while the incidence of diseases of old age has increased.

There are some diseases associated with a modern lifestyle that were very rare in the past. Type I diabetes was almost unknown before the 20th century. Heart diseases have increased significantly since the industrial revolution, and seem to be increasingly affecting younger people. Some types of cancers have increased, specially cancers associated with environmental carcinogens. Living longer also makes people more prone to cancer.

Allergic rhinitis (hay fever) has become very common, affecting about a quarter of the population of the US today. It was much rarer in the past. In fact, even today, it’s almost unheard of in many poor countries.

In general, allergic diseases have increased, especially in western societies. This may in fact be due to a reduction in other diseases, mostly worms. A few hundred years ago, almost everyone had a few worms in their intestines. Worms are very important in modulating immunity, and the loss of worm infestations may have made people much more susceptible to allergies. Aside from worms, gut flora (bacteria) also modulate the immune system, and the reduced range of gut flora species in western populations probably increases allergies.

While infectious diseases have more or less become a minor problem in the west, chronic childhood diseases are on the rise. Childhood obesity is up fourfold in the past 50 years, asthma has doubled since the 80’s.

It’s not obvious how to make comparisons across a long time span. You could divide by age group, for example. If you look at young children, modern kids are much better off. They may have more allergies or asthma or may be out of breath and chubby, but most will survive to adulthood. You couldn’t say this a few hundred years ago.

Young adults were probably healthier in old times, if they weren’t starving to death of famines or dying of plagues. This is the peak period of fitness in humans, and while they still suffered from the occasional infectious diseases, their more active lifestyle and healthier diet probably meant that they were healthier than their cohort today.

Middle age would be much the same, better in some ways today, worse in others. Again, the more active lifestyle and hard physical labor of the past was conducive to a healthy middle age, but this is also when problems start to catch up with you and lacking a modern medical infrastructure, were allowed to get much worse than today.

In old age modern people would be significantly better off. This is when people start to develop serious chronic conditions even despite their healthy lifestyle in the past, and modern medicine can be a great help.

Aside from such broad generalities, you would have to narrow your question down to some specific time and place and age group to get more detailed answers.