In the context of the seventeenth century, there was extensive difference in equipment and costs between dragoons and cavalry. Now, this was also the period where most cavalry became the type known as harquebusiers, where the distinctions between cuirassiers, reitters, and other forms of cavalry disappeared or merged into an all purpose cavalryman.

If we take the British Civil Wars for an example of the differences between the mounted soldiers of the middle of the seventeenth century - cavalryman and dragoon.

The cavalryman of the period needed a steel helmet, usually with a three-bar or single-bar face guard, and either a 'corslet' (back and breastplate) or a strong 'buff' coat of leather armour. A well-equipped trooper might have armour over a buff coat, and strong leather boots and gloves.^(1) His weapons would include a good quality sword, as well as flintlock carbine, and usually two flintlock pistols (although older wheellocks might have been used in a shortage of the new flintlocks). The flintlock was more complex and more expensive than the matchlock firing mechanism carried by the infantry. A flintlock in 1643 would cost £1 2s, whereas a matchlock only 12s 6d.^(2) The dragoon on the other hand, would be equipped almost identically to a conscripted foot soldier - minimal uniform, shoes, a cheap short sword, and a light matchlock musket and associated equipment. As the wars continued, dragoons often re-equipped with flintlock muskets but otherwise remained equipped as Poor Bloody Infantry.

The dragoon's horse was only as a means of transport - less attention was given to quality of the horse, or requirement of speed, strength, and agility. In comparison the cavalryman's horse needed to be 'serviceable', of a certain size and strength to carry the cavalry man, at the charge, into battle and on his myriad other duties. It therefore needed to be around 15 hands high, strong, but nimble. The difference can be seen in the prices paid for the different mounts with the New Model Army paying £7 10s for a cavalry horse, and only £4 for a dragoon horse.^(3) Even cavalry saddles cost more, as the saddle of a trooper needed to be higher, reinforced, and more substantial because the cavalryman relied on it for much of his movements and strength when riding into battle, whereas dragoon saddles only needed to be riding saddles. According to Peter Edwards in his review of Civil War Equipment, dragoon saddles cost half of what a cavalry saddle cost.^(4)

Dragoons were, for the initial century or more of their inception considered inferior as a mounted arm to cavalry. Even one of their earlier adopters, Gustav Adolphus of Sweden referred to them as "labourers on horseback."^(5) As the 18th century advanced, however, armies began turning the dragoon more toward a cavalryman that could also fight dismounted in addition to mounted rather than simply a mounted infantryman who only fought on foot. Their equipment became more in line with cavalry - longer sword, boots, better quality horses, etc.^(6) By the time of the Napoleonic wars, the dragoon of old, originally simply mounted infantry, had become a subset of the cavalry itself, the name applied to particular type of cavalry regiments as the cavalry arms diversified once more into various regiment/equipment-specific roles of Heavy Cavalry, Light Cavalry, Dragoons, and Lancers.^(7)

1. See descriptions in both Firth, C., Cromwell's Army: A History of the English Soldiers During the Civil Wars, the Commonwealth and the Protectorate (Methuen, 1902) and Young, P., & Holmes, R., The English Civil War (Wordsworth Editions, 2000)
2. UK National Archives, State Papers, 28/11, i, f.9, receipts to the New Model Army 1645
3. Edwards, P, 'Supply of Horses to the Parliamentarian and ROyalist Armies in the English Civil War', Historical Research, 68 (1995)
4. Edwards, P., Dealing in Death: The Arms Trade and the British Civil Wars, 1638-1652 (Sutton, 2000), p. 12
5. Brzezinski, R., The Army of Gustavus Adolphus (2): Cavalry: Pt. 2. Men-at-Arms (Osprey Publishing, 1993), p. 38
6. Barthorp, M. British Cavalry Uniforms Since 1660 (Littlehampton Books, 1984)
7. Rothenburg, G., The Art of Warfare in the Age of Napoleon (Indiana University Press, 1978)

It's the difference between getting a car that can do drag racing versus getting a car that's just for getting you to work and the supermarket. These may be tasks that look very similar to one another, but one calls for specific challenges that you need particular qualities for. These two posts, while general overviews, also provide a look at the dragoons and how they are different from the other cavalry types.

• u/Bacarruda has an overview on the various types of cavalry of the Napoleonic period;
• and u/waldo672 has an overview of their own of the cavalry types as well.

I should note that there may be some qualities that are unique to the Napoleonic period, so if anyone else wants to give an answer of their own, please don't let this post stop you! More information is always welcome.