watts or joules?

I have a pair of martin logan aerius speakers,the local dealer here told me a long time ago when I know that I need a lot of power he recommended ARvt-50,but I said it's only 50watt? He said yes but its high current and that is what I need that amp has some 360 joules of power Ihave heard AR's ca-50 same 50 watts but only 160 some joules and it souuded very weak,Some amp companies don't even know or underwtand about joules,an old carver amp used to measured in joules only.As of my knowing only Audio Research,and Carver list joules of power,Why? Any insight to this ?Thanks Nick
In those applications there is little to no difference -- just the way it's expressed.

Joule is a unit of energy (i.e. it takes 1 joule of energy to exercise the force of 1 newton for a displacement of 1 metre).

In electronics it related to Watts as follows:
1 joule= the equivalent of 1W of POWER per second required to produce 1Watt in one Second. Similarly, Watt is the product of amperes times volts (voltamperes).

Basically, you can look at a power supply's watt rating and be just as well informed. Much of the stuff you see is mumbo-jumboed to sound more scientific and different, and, thereby, more luring than it actually is.
I believe in the situation you describe the difference is that watts are being used to describe the continuous energy delivery ability and joules are being used to describe the instaneous energy delivery ability.

Watts or joules or amps could have been used to express both.
A joule is one watt multiplied by one second (watt-sec), or energy consumption over a period of time. This is what your utility company bills (a kilowatt-hr is 3,600,000 joules). Or, the units of joules is voltage x ampere x time.

The different joule rating of the amps reflects the amount of time required to deliver a given current (based on the speaker impedance only) at a constant voltage. To oversimplify: if volts times amps is constant, the difference is in current delivery time. This is determined mostly by the power supply capacitance.

This time difference is the equivalent of having power in reserve for transient spikes that exceed the steady power rating of the amplifier. The capacitors trade voltage for current and discharge the energy as the speaker calls for a transient spike. If the caps have the joule rating to do it, the spike is transduced and you hear a nice attack on the instruments played.

The power that the speaker draws to produce sound is determined only by the amplifier output voltage and the speaker's impedance. But this is steady power - constantly available at a given impedance. A variation in the speaker impedance causes the current demand to change. A lower by half impedance at a certain frequency will cause the current draw from the amp to double, if voltage remains constant. This extra current has to be available either from the power supply capacitors or transformer. It it's the transformer that's capable, the higher current will flow all day long (the joule rating is infinite since the joules are transferred as long as the amp is playing). But if the extra energy is stored in the capacitors, the joule rating dermines how much and by how long you can have the extra current for. This is basically the headroom that an amp has.

The bottom line is the 360 joule amp will perform better if and only if the power rating and transformer VA ratings are identical, all other things being equal - which is rarely the case.
Joules sound impressive to the person who likes tech terms. Bottom line is how many amps and volts does the amp deliver into what load. This also means continous and peak voltage and amps. These are electronic specs that not necessarily dictate the ultimate sound. The speaker load is very important for any amplifier and what it can drive.
Only my opinion
Watts. The output power of an amplifier is never specified in joules. Joules refers to the amount of energy storage that is in the filter capacitors of the power supply. Generally a higher number is better, but will not tell you much except in comparison to other amplifiers of similar power.

Being that there are a variety of other things that can also affect the way an amplifier sounds, I would not put too much weight on joules alone. Like any other human endeavor, it pays to educate one's self about what is possible rather than hang your hat on one specification over all others!

Above all have fun!
my question still remains,why does the arc ca-50 sound not no where as good as the arc vt-50,arc tell me that they are identical except for the joules,and that joules or current will give you transients,attack,and hidden nuances,and that makes all the diff,. Rogue audio make a tempest at 90 watts per but they do not address the joules question,I am let ato believe that while many amps are great arc is the best!,Nick
"My question still remains ..."

My simplistic response is that an amp with a 50 watt rating might not be able to handle certain music peaks. 50 watts alone might not be enough. The 50 watt rating is how much power the amp will deliver on a steady state basis into a purely resistive 8 ohm load (versus a more complex load like a real speaker) at a mid-band frequency. What happens with a complex load or a load where the impedance drops below 4 ohms? The amp might run out of steam. The joule rating applies to the power supply, actually to its capacitors, and gives a measure of how resilient the amp is when dealing with complex music material with significant peaks when driving a complex load like most speakers. I won't repeat all the fine explanations of the preceding posters regarding what a joule is. My bottom line is that an amp rated at 50 watts might not be powerful enough for some music peaks. Whether it can perform well depends on design decisions that can be partially described by certain statistics, like the power supply's joule rating.
The VT 50 has a better power supply.....