This is a difficult question to answer, but allow me to try and put some context around it for the period of military history I am most familiar with - the early modern period in western Europe.
The physical demands of a soldier were high - sickness, infection, bad food and water, exposure to the elements, all of these were daily risks to the soldiers of the past - only a small percentage of men who died in war did so due to the battlefield, many instead died or were disabled due to the myriad other ways that fate could come up with. This problem was widely accepted and understood by contemporaries, in the advice of Gervase Markham in his Soulders Grammar 'who knoes not that sicknesse, mortality, slaughter, ill diet and lodging, hunger, cold and surfeites doe so attend upon Armies, that by them commpanies are exceedingly weakned and made lesse, so that he which mustereth one hundred men if he bring scree score and ten able men into the field to fight, is oft held for a stronge company.'^(1)
In order to limit the chance of men falling sick or ill, recruits were expected to be in good physical condition with the Privy Council of England stipulating that that only 'fit and able men' should be selected, being particularly concerned that men deemed 'unnecessary', unemployed, or wastrel should not be sent.^(2)

However, the sheer risks of a soldiers life (the Markham quote suggests a wastage of at least 30% on average) meant many people did everything they could to avoid service, leaving the poorest and meanest of society to be sent to the wars, particularly in times of impressment or conscription. This could account for a degree of the wastage as many of the men sent to war would have already been unprepared physically to survive it being poor, ill, or just underfed before they even put on a uniform.

Those soldiers who got better from wounds or illness would return to service, while those that only partially healed would be discharged, the rest died. However, surviving petitions of veteran soldiers of the period reveal that soldiers would not be discharged until they were of no further use to the army, incapable of serving. The Royalist soldier Martin Prince was ‘wounded at Edgehill [October 1642] in his head and was wounded at the storming of Bristoll [July 1643] in his shoulder; and was wounded again at Alesforth [March 1644] … in his knee of which he was ever since Lame’^(3) While Wilde Robinson of Staffordshire received ‘many and sundry wounds’ when he served as a soldier for Parliament, ‘both in England and Scotland’^(4) These types of sources reveal that soldiers had access to some rudimentary treatment, enough to survive battlefield wounds, returning to service as soon as possible (they would not have been paid if ill too long) but as soon as they were perceived as 'lame' they would usually be discharged. As these men were private soldiers, they would still have been expected to serve in frontline duties, whatever their aches and pains.

To you original question "were they fitter than us" it is difficult to answer as what you mean by fitter or healthier can throw off the reckoning - our access to modern medicines and healing trumps their own. However, they would certainly have been hardier, living in a world where nursing and care was limited to the very wealthy - for everyone you carried on through the pain and discomfort which you could do nothing about, or you simply died as a result. Whereas we can expect through physiotherapy, pain medication, changes in diet, doctor referrals etc. to try and mitigate it at least. Which I suppose could argue for them being a form of healthy - you were either were healthy enough or you would more than likely be dead in time. 'Fitter' would be a difficult term - their diet would not have allowed for excess fat and their lives, both in and out of the military, would not have been able to be slothful (usually) however the majority of the population lived almost at a subsistence level where simple failures to us which could be replaced relatively easily (a broken oven, accidental wastage in food stores, bad weather for the crop), would have led to several days without food or even starvation, impacting their overall fitness. Hard lives, hard people. I know I have not really answered your question, but the differences in lifestyles and the context of living between then and now make direct comparisons almost guesswork other than, broadly - I am very bloody glad I'm not them having to do what they did.

References

1. Markham, G., The Second Part of the Soldiers Grammar: Or a Schoole for Young Soldiers … For the Training, and Exercising of the Trayned Band, Whether They be Foote or Horse (London, 1627), pp. 47–48

2. The National Archives (Kew) SP 16/72/48, Secretary Coke to Secretary Conway, 31 July 1627

3. ‘The second certificate for Martin Prince of Barwick in Elmet, West Riding of Yorkshire, January 1670’, Civil War Petitions

4. ‘The petition of Wilde Robinson of Draycott in the Clay, Staffordshire, 14 July 1657’, Civil War Petitions