They use different mechanisms to measure the velocity. The shadowgraph velocity measured based on two frames of shadowgraphs, and PIV obtains the velocity based on the tracking of seeding particles. They have their own respective virtues. For shdowgraphy, it is better for high speed flow velocity measurement and can visualize the spray shape clearly. PIV can also obtain vorticity etc. parameters except velocity.

For your case, If possible, I suggest you use both firstly. Based on measured results, then decide to focus one method.

People usually do not use the shadowgraph to measure velocity, since it's not a good way to obtain the accurate velocity vectors in the flow field. The spatial resolution is also a limitation for velocity measurement. PIV as a method to capture the instantaneous velocity has been widely applied in measuring the low- and even high-speed field, provided that the following features of the tracing particles fit the need for high speed measurements. So if the condition permits, PIV is a better choice.

PIV is a opt method to measure the velocity and also flow pattern. Shawdowgraphy doesn't give that much accurate results, however it give accurate results on other parameters like cone angle, spray structure, instability / surface waves. If possible go for PDPA  since it give droplet size and velocity rather than PIV. 

 The two methods measure the velocity based on different principles. PIV method determine the velocity value with the interpolation algorithm of  the tracking of seeding particles. So it can capture the whole velocity field distribution, turbulent fluctuations etc.. However, PIV's measurement accuracy is affected by the interpolation algorithm. The velocity information measured by the Shawdowgraphy method is relatively less.

I'll just add here that in some applications, e.g. microscopy, it is fine to obtain shadows of particles using backlight illumination (the fluid has to be transparent and particles opaque). Then it works almost the same as PIV if the images are inverted. OpenPIV (www.openpiv.net) can do the job even without inverting images [disclaimer - I'm one of the authors, just happen to know how the code works]

Shadowgraph method is not a good choice. It does not get the real velocity because it map a 3-D flow into a 2-D plane. So i recommend you use PIV.

Actually, the previous comment points to the right direction, if the optical system is based on shadowgraphy, the perfect match is then a 3D-PTV. Of course it needs more than 1 camera (or some optical setup that create a sort of virtual multiple views for 1 camera), but then you'll get 3D positions of the shadowed particles and get the full field. See www.openptv.net for more details [disclaimer, i also co-develop that one :)]

For 2D fields there is the fundamental difference, that during PIV the particles are illuminated by a laser sheet and thus the cross correlation is calculated only from the particles in your plane of interest. Shadowgraphy however (such as Schlieren) is a line-of-sight averaged technique, where all density fluctuations in your flow are projected on an image plane. If you do your cross-correlation on these Shadowgraph images, you will take into account all movements in the other planes of view, which will falsify your results. Taking this difference into account I would definitely go for PIV.

I also agree with the previous answer, that for the use of Shadowgraphy for velocity measurements, a 3D technique would be a good choice.

Unless there is a very short depth of focus that can help distinguishing between particles within a focal plane and outside of it. Also a sort of 3D (depth) information.