When buying a portable air compressor for your vehicle to air up tires...?

The clips will carry more current but this doesn't necessarily mean it will have more inflation capacity. Most manufactures don't rate these mini compressor in CFM they use PSI which is kind of useless for figuring volume transfer rates. The problem with either flavor of 12vdc compressor is they take forever to inflate a regular tire if you are looking to air up 4 off-road tires it can take 15 minutes or more per tire depending on their size. Most Harry homeowner versions won't hold up to constant use but if you can jack the vehicle enough to take the weight off the tire it will go a lot faster and put less wear and tear on the compressor. If you're on uneven ground be careful you don't need to jack the vehicle very much just taking most of the weight off is good enough.

>what if you had a 12V Battery Clip-On and Cigarette Lighter Adapter?

For continuous duty I'd try to use the clips as much as possible they carry the most current cig adapters only carry 1.5 amps before they pop a fuse, factory 12vdc power ports only carry up to about 5 amps. Light duty battery clips can carry 20-50 amps heavy duty clips can carry 100 amps or more. If you use an adapter make sure you have a few spare fuses on hand just in case. Speaking of fuses most of the 12v compressors I've used had internal fuses if it stops working take it apart and look for a blown fuse. Sometimes the fuse is soldered in but if you have a soldering iron it's a 10 minute fix. If it isn't the fuse then the compressor probably seized from overheating that usually trashes them. I always carried a bicycle pump as a back up it sucked but it was better than nothing when my compressor finally gave out its last wheeze it is really important to jack the weight off if you have to resort to hand pumping (but it will get you back up to highway speeds).

One difference is the power of the compressor...

Compressors that use battery clips have more power than those that use a cigarette plug and they are faster.

Next difference is that the cigarette lighter wasnt really designed to be used for that purpose, the fuse is low amp and the wiring is not heavy duty and the compressor could blow the fuse or heat up the wiring and cause a fire or melting of other wires ect.

which is why many vehicles have a separate socket from the cigarette lighter called a power socket which has heavy duty wiring a higher amp fuse and is made for using compressors and other things that have a cigarette type plug in.

Convenience. If you use the cigarette lighter, you don't need to lift the bonnet or play with the battery. Much simpler and safer.

The battery clip on ones will give you more current and are generally more heavy duty and expensive.

If you have a 4wd, definitely get a heavy duty one, for a normal car, well I've had my $50 DrAir for the last 20yrs and it still pumps tyres up ok.

Battery clips can carry more current so a compressor with them might have a larger capacity motor.