I'm not overly concerned with one country so examples from anywhere including the United States would be great. My question is this, what would be a more likely career?? for a man of wealth or an aristocrat/"poor" or minor aristocrat(such as Lord Keith). My understanding is that the navy at least in the British RN, that there would have been more "social"? mobility for someone in the navy with talent since the navy had done away with the buying of commissions. I assume it would depend on the individual's wealth and connections but seeing as both the navy and the army during war could be very deadly even to an officer. (I may be off on this part since I am mostly thinking about of the battles during the Napoleonic wars,higher usage of rifleman and battles such as the siege of Badajoz.) If one would have been seen as more suited to a certain social status compared to the other. Such as those with more wealth or connection would end up in the army and that the navy was seen as a place for people bellow "their" own social status had to go.
From what I've read of the French and British accounts the army was the most popular; with light dragoon (British) and cavalry (French & British) especially. Otherwise, it was guards regiments of foot (eg, Coldstream Guards, the Consular/Imperial Guard) and then grenadier or skirmishing companies of the line. Artillery was a poor third and Engineers a distance fourth (despite Marshal Berthier have a whole company of engineering officers as his aides/guides, but that's a staff appointment and so doesn't count!).
I can't say exactly for the Navy but before scurcy was understood and was effectively cured, it was always a poor second choice. The Navy demanded people of ability, navigation was very mathematically intensive, as well as being able to manage a crew of 200+ men, stores, supplies, tide charts etc...and the list of post-captains in the RN was only about 200 names long!
Sources: dispatches, Memoirs of Elzear Blaze, Memoirs of Baron de Marbot, "Scurvy: How a Surgeon, a Mariner and a Gentleman Solved the Greatest Medical Mystery of the Age of Sail"