It gets terribly confusing when it comes to lighting in photography. One of the area, out of many is, whether to use strobe lighting or speedlites or continuous lightning for studio and outdoor photography.
There is no golden rule of lighting in photography. It is all based on personal taste, requirements, types of photography. One or more combination of these lights can be used to come up with amazing results.

Price is one of the major factor on these types of lightning.  Continuous lightning is cheap or can be achieved as home DIY project. Speedlites are in the mid-mark whereas strobes are expensive.

 

Continuous lighting

Pros

• What you see is what you see –  you can see by your naked eyes what you  can get on the picture you are capturing.
• Built in light meter – camera can utilize built-in light meter to decide f stop, ISO.
• Non-Burst of light  – Burst light startles subject like baby and animals
• Power consumption -Modern energy efficient light bulb makes it greener and less electricity bills
• Video shooting – burst lights are not total no-no for video shooting.

Cons

• Unable to freeze motion – due to limited power camera setting needs to be low f stop and higher ISO

Ideal for: Product photography, Videos

 

Speedlites

Pros

• TTL Metering – helps to easily set correct exposure
• Portability – Compact to carry and add more than one speedlites
• Shorter Flash Duration – distinct advantage to freeze motion
• Sync and Control -Speedlites are controlled using Camera or back of the speedlite. You can set master and remote to control other speedlites available. Exposure composition, high speed sync are controlled from the camera. Limitation with Speedlite is that it has to be in the line of sight, to overcome the issues companies invented radio signal pocket wizards.
• Power – give 150 Watts seconds of power and scalable with additional speedlites, subjective view according to the type of photography

Cons

• Recycle time/Refresh rate – takes about 1-2 shots per seconds
• Battery – they are battery powered so need to carry large number of batteries
• Inconsistent Color temperature & Exposure – Once strength of battery getting low

Ideal for: Outdoor or mobile setup, Wedding shoot

 

Strobe lights

Pros

• Power – can give upto 600 -4800 watt Seconds depending upon model
• Recycle time/Refresh rate – Upto 10 shots per seconds on high end models
• Sync and Control – Historically controllerd with Sync cable. Pocket Wizard which controls strobe wit radio signal,, all it does is send instruction to stobe to fire. Majority of the studio light cannot be controlled to turn on/off modeling light,control power etc apart form few exceptions like ProFoto Air.
• Light modifiers -Softbox, umbrella, reflectors have more source options like 15 foot
• Consistent Color temperature & Exposure – generally, runs on AC power hence no power degradation

Cons

• Manual Metering – need to calculate and set manually on the strobes and camera
• Not portable – bulky with modifiers, Heavy, Battery packs is required

Ideal for: Portrait, food, cars, photo shoot