Of these two spells they are both similar in that they have a tracking component. HM gives advantage on tracking survival checks, while LO just gives you the location within 1000 feet. The pros of HM is the range of 60 feet, extra damage and the cheaper slot, the cons are that it ties up the bounes action, concentration and the possiblity that your target may escape. In contrast the advantages of LO is the certinty of finding the object, it can be used any object that you've seen recently and allow have to do is plant it on your target. The consequences though is that LO is more expensive as a 3rd level spell slot, and ties down concentration (although since you know the object you can always recast the spell.)

Hunter's Mark

Pro: Can last for up to 24 hours.
Con: Must have actively seen and marked the target earlier in the same day.

Locate Object

Pro: Works with a vague description for an unknown item.
Con: Must already be within the target's vicinity.

 Basically, Hunter's Mark is good for chasing a mobile target (Hunting) while Locate Object is good for treasure hunting (locating objects).

I haven't found Locate Object to be much good for anything. You're better off just using your eyes, even if your whole party's Perception isn't very good.

Locate object is useful for finding pickpockets.

Hunter's Mark won't help if the target travels in a way that can't be tracked (flight, teleportation, walking through walls, etc). Locate object is only useful if the target actually has something distinctive that you can track (and they don't have a lead-lined bag or something similar). You don't get any terribly reliable tracking spells until Locate Creature.

Also Hunters Mark doesn't tell you where your target is, it just gives advantage on those checks to find it.

A thousand feet is less than a fifth of a mile or a third of a kilometer. That's less than the length of three NFL football fields with half of the end zones included. That's about what most people (real world, no game stats being applied) can cover at a brisk walk in less than five minutes. In game terms, a person with a 30 foot move can cover that distance in three minutes and eighteen seconds without using the dash action. It ain't far. For locate object to be useful you have to already be close to what you're seeking. So it can be helpful if you're looking for a magic idol or whatnot in a dungeon, or something specific a person is carrying in a crowd that you're also in (like Lunali's pickpocket example). Finding somebody in the wilderness or a large city (even a decent sized town) based on a distinctive piece of jewelry or such, not so much.

If you're hunting a person over a long distance, hunter's mark will ultimately be more helpful by virtue of being any help at all, but does require a character with a good Survival bonus to reliably benefit. Also you have to have been close to the target and then let them escape in the first place.

LO would be so much better if you could increase the range with a higher spell slot. Every single time we've wanted to use it we were looking for something over a much larger area. As it is written, it's so situational that you almost need to craft the situation around the spell to create a case where it's useful - that situation usually being that someone just stole something from the party and disappeared into a crowd or into the brush.

At a certain point you just need Scrying. Though of course there's effects that block that as well.

Quote from Pantagruel666 >>

At a certain point you just need Scrying. Though of course there's effects that block that as well.

 While running CoS, the party used Scrying on Strahd to get a view of where he was (currently) in the castle and then used Locate Object on one of the decorations within that room to figure out how to find their way to Strahd (thus saving them from having to scan the castle top to bottom). 

Of course, this strategy wont always work. For characters like Strahd, legendary resistance may prevent your scrying from working in the first place (I did not use his in the above situation because I figured there would be more crucial saves for him to make later on in the encounter, and I thought it was a clever solution for the party to use). 

Locate object is very useful for reverse-pickpocketing. Drop a ball bearing in a henchperson’s pocket or saddlebags and discreetly follow them to the BBE’s hideout from the relatively safe distance of 1,000 feet. (Like in the movies when they plant the tracker on somebody’s car, or whenever Spider-Man tags someone with a Spider-Tracer.) It is especially useful if someone in the party is an Arcane Trickster with Legerdemain.

Another alternative I’m surprised nobody has mentioned is Mind Spike. Provided you can cast it without being noticed and initiating combat (perhaps with Subtle Spell if one is adept at Metamagic), the Target gets a sudden excruciating migraine and if they failed their save you simply “know” where they are for an hour unless they plane-hop. It’s less clandestine than either of the others, and you might have to deal with repercussions, but it’s only 2nd-level and I do loves me my multitaskers.

Whenever I have to make decisions like this, I always assess which will likely be the “better investment” given certain criteria:

• The character’s total number of spells known/prepared.
• Their overall number and level of spell slots they'll have.
• And most importantly, what the rest of the party can do. (I believe a party works best as a superhero team rather than a “team-up” if you catch my meanin.’)

If my PC’s known spell count is gonna be tighttight (like a Sorcerer, or a ½ or ⅓ caster), I tend to go with the multitaskers. If I only get to pick up a few tools to stock my PC’s itty bitty toolbelt, I wanna know they can do as many jobs as possible with those tools as possible.
   If my PC’s total pool of spell slots is gonna be pretty low (like those ½ & ⅓ casters again), I also tend to add weight to lower leveled spell since it’ll be easier to squeeze them in in a pinch.
   If my character has spells known and spell slots for days (like da Wiz), I frequently go for the more effective, specialized spells since I know I'll likely not have to worry as much about if I’ll be able to cast it. Since that’s not a concern, I know I’ll appreciate having the better tool to use for the job because they have the equivalent of a fully stocked work truck at hand.

However, if the party already has a Ranger with HM, or a Wiz with LO, I would pro’ly take the other spell instead since in 5e, redundancy is less beneficial IMO than diversification. (If there’s a chainpact Warlock in the party I wouldn’t worry about it at all and instead look to fill some other unfilled need for the team. Chainpact is just that damned good, it’s a well-stocked toolkit all by itself.)

Instead of Hunter's Mark, if you've seen the opponent, then Mind Spike would be a better way of following.