planning on buying.1000 dollar budget.
Delta will be more accurate due to no x/y axis. On a Cartesian the belts on the x/y will slack a little and distort prints. That is way less prevalent in a delta
To give you a reason, the advantage for a Delta bot is movement speed. This is why they were invented (it is for more that 3dp). But in 3dp the movement speed is limited by the extruders ability to melt plastic, not the motor controllers. So the advantages of the Delta are limited.
Here are some remaining arguments and counter points:
Delta printers can be infinitely tall… This is actually not true, they need to be more ridged when they are made tall. And a tall delay is less economical in a cost per unit volume. And print times are really long for tall prints.
Delta’s are cheaper… A solid Cartesian printer can be made from the bom of a Delta with similar size and print quality. This is a wash either way.
Organic prints are better… Not at all, the Delta’s infact have more estimation error. This is because the slicers make Cartesian slicers, which the printer takes and concerts to Delta movements. So rounding error is added to the system.
But there are some complexities:
Long Bowden tubes make printing hard
Print head must be as light as possible
Computations take more processing power.
The arms can flex.
Homing and calibration are more difficult
The print volume is a weird triangular cylindrical shape.
Resolution of the printer is dependent on the xy location of the part. (More steps per millimeter near the middle, less near the edges)
@Abc_Def that is a myth, the xy resolution of a Delta is dependant on the bed position. And a belt driven Delta will have the same effects on all axis… This effect is amplified on the edges of the printers bed,
One of each. But the delta is far more mesmerizing to watch. 
I am surprised by the interest in deltas b/c of the finicky, obscure nature of it. I wonder if new buyers are simply taken with the fancy movement. Guys that have both already tell me they are fun but their go-to is Cartesian. Since I’m a simplicity minded guy, Cartesianism with direct drive have always seemed the most straight forward with the least variables to chase. Speed is always considered slow by newbies- it’s all relative. Our new Tinyg electronics does speed things up w/o resonance showing but, hey, it’s all slow to the masses used to just buying at target. I’m just happy having a 3D printer. ANY 3D printer and I wouldn’t discourage anyone taken w deltas. I say, print! Use what you have. Master it. The best tool is the one you have and know how to use.
Brook
I have both and i usually use the Cartesian, but if I need perfectly round or mechanical parts I use my delta. (The Cartesian just won’t do circles. Tried everything)
Deltas are not a “hobby” within the hobby of 3D printing by any means. It’s just as popular as regular cartesian printers and we have the sales figures to prove it.
There’s also nothing complicated about a delta printer. Maybe in the beginning when they were coming out, they required manual work. Nowadays, you’ll find that most deltas do auto-leveling far better than some cartesian printers. And they are definitely far more precise per speed in comparison to a cartesian. There’s nothing finicky about deltas.
All 3D printers have their own idiosyncrasies. Deltas have more than Cartesians.
They are tall.
Bowden tubes in any bot have more friction and don’t do flexible filament near as easily, if at all.
Weird shape on the build platform
Harder to calibrate
Not as easy to understand as simple X, y, z
Harder to ship as assembled units - especially really big ones. They lend themselves to kits which are dying out, sadly.
Not all software supports them
Requires more processing power for faster speeds
I think sales show the impact of these things.
I love to watch them. they are really intriguing. I think they will have a niche for a while but grow more rare as time passes. As harsh as it sounds, they aren’t the future of 3D printing
One comment from a delta owner caught my eye- (paraphrase) … No delta can print better than a good Cartesian so I mostly use my cartesian… He did mention the stationary bed on the delta is nice and it was great for really tall objects, but not for mechanical parts requiring strict tolerances.
All that said, there are some terrible Cartesians out there. Both styles, if done well can produce great parts.
Brook
I think the single great thing about a Delta is the static bed. This affords you the possibility of having a stable build platform.
Combine that with electronics that are capable of doing the required mathematical transforms, at speed, and there is great scope for the Delta.
I agree with @Camerin_hahn that most slicers are not ideal for Delta machines but if someone put the effort into addressing that then results would be even better than currently achievable.
I don’t know about Deltas waning, I think they haven’t yet come-of-age.
I agree with @Brook_Drumm . Deltas have their place and may offer more in the future, but cartesians’ are more adaptable to modifications beyond 3d printing. Laser, mill, 5th axis, extending build area, filament extruder, etc… I see the all-in-one home hobby tool being a cartesian, not a delta.
An IPod is cool, but tech always crunches more adaptability into single devices, i.e. IPhone.
Open source is also a plus, helping make mods easy and cost effective, that’s why “sales add” I created the all-in-one opensource Reach 3d printer.
I would choose a 12" Prusa, with a real nice structure if this is a budget for a first printer! Delta’s are good looking 
but if you are a beginner I heard that Delta’s were not meant to be used as a first printer at all. On the other hand I reviewed a lot of posts about both printers and all have more pros than cons.
I like the new Makerfarm Pegasus, the Prusa i3 from the original PRusa is also very good and both can get up to 0.05 microns (nobody uses eheheh) .
@Shai_Schechter I know you and several others are committed to Delta printers, I still don’t know why. They have most of the same issues with a few extras.
@Camerin_hahn and @Brook_Drumm are correct about everything. I have multiple Deltas and multiple Cartesian printers. People who think Deltas are more accurate or faster than Cartesian are simply using low-quality Cartesian printers. Both can be great, but high-quality Deltas are much more reliant on fabrication precision, probes with auto-calibration routines, and 32bit processors to churn through all the extra math. You don’t need that stuff to get great prints from a Cartesian printer.
Some specific points:
- If your Cartesian printer can’t print circles, it’s because your system has mechanical backlash. Deltas can have backlash too.
- If you think Deltas are faster, you’re not trying to print near the edge of the build plate where near-horizontal arms cause your motors to run 2-3x faster than the end-effector. That can be a big issue on 12v systems in particular because the motors rapidly lose torque at high speeds. Cartesian motors don’t have to run as fast for a particular feedrate, so their top consistently-achievable speeds (across the whole build area) are actually much higher.
- If you think Deltas are more precise, you’re ignoring the very low Z resolution that most of them have – 100 or 160 steps/mm are common, compared to 400-1600 steps/mm for Z in most Cartesian printers. That affects minimum layer height and first-layer quality. And don’t get me started on the likelihood of getting skewed and off-tolerance prints when you fill the bed on a delta…
@Abc_Def that is the only valid argument for Delta printers over Cartesian printers. And it is not a bad one.
But I would never recommend a printer to a friend because it looks cool, it has to work well.
Selling person new to printing a Delta because it looks cool is a great way to make sure they hate printing. People want ease and reliability out of their first printer (because they don’t yet know what pain is)
For companies to survive in this market, you MUST differentiate yourself from competition. A new buyer facing the delta verses Cartesian question will more likely buy a Cartesian.
Some decide to indeed go with delta- and at that point, the company selling them needs to stand out. If they do, whether in resolution, size, ease of use, customer service or price- then they can sustain business for a long time as they dominate a niche. Proximity to the buyer matters too. So perhaps a better question is what IS the best delta for a first time delta buyer. If they do research, maybe they know they are unique and they want one. So if their eyes are wide open - point them to a great company and design and wish them well.